##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! // BEGIN FIRST INPUT BLOCK Digits = 32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start = 0.1; x_end = 10.0; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); // # testing comment glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 10; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; glob_max_minutes = 1; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y1 (double x) { return(1.0 + cos(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % h = 1e-05 x[1] = 0.1 y1[1] (analytic) = 1.995004165278026 y1[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10001 y1[1] (analytic) = 1.995003166894109 y1[1] (numeric) = 1.995003166894109 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099843366683489 y2[1] (numeric) = 1.099843366683489 absolute error = 2.220446049250313e-16 relative error = 2.018874793004329e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10002 y1[1] (analytic) = 1.995002168410692 y1[1] (numeric) = 1.995002168410692 absolute error = 2.220446049250313e-16 relative error = 1.113004328721717e-14 % h = 1e-05 y2[1] (analytic) = 1.099853316710166 y2[1] (numeric) = 1.099853316710166 absolute error = 2.220446049250313e-16 relative error = 2.018856528879703e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10003 y1[1] (analytic) = 1.995001169827775 y1[1] (numeric) = 1.995001169827775 absolute error = 2.220446049250313e-16 relative error = 1.113004885827711e-14 % h = 1e-05 y2[1] (analytic) = 1.099863266726857 y2[1] (numeric) = 1.099863266726857 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10004 y1[1] (analytic) = 1.995000171145358 y1[1] (numeric) = 1.995000171145358 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099873216733562 y2[1] (numeric) = 1.099873216733562 absolute error = 2.220446049250313e-16 relative error = 2.018820001676797e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10005 y1[1] (analytic) = 1.99499917236344 y1[1] (numeric) = 1.99499917236344 absolute error = 2.220446049250313e-16 relative error = 1.113006000207905e-14 % h = 1e-05 y2[1] (analytic) = 1.09988316673028 y2[1] (numeric) = 1.09988316673028 absolute error = 2.220446049250313e-16 relative error = 2.018801738598501e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10006 y1[1] (analytic) = 1.994998173482023 y1[1] (numeric) = 1.994998173482023 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099893116717009 y2[1] (numeric) = 1.099893116717009 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10007 y1[1] (analytic) = 1.994997174501106 y1[1] (numeric) = 1.994997174501106 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099903066693749 y2[1] (numeric) = 1.099903066693749 absolute error = 2.220446049250313e-16 relative error = 2.018765213488183e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10008 y1[1] (analytic) = 1.994996175420689 y1[1] (numeric) = 1.994996175420689 absolute error = 2.220446049250313e-16 relative error = 1.113007672198711e-14 % h = 1e-05 y2[1] (analytic) = 1.099913016660498 y2[1] (numeric) = 1.099913016660499 absolute error = 2.220446049250313e-16 relative error = 2.018746951456145e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10009 y1[1] (analytic) = 1.994995176240773 y1[1] (numeric) = 1.994995176240773 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099922966617257 y2[1] (numeric) = 1.099922966617257 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001 y1[1] (analytic) = 1.994994176961357 y1[1] (numeric) = 1.994994176961357 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099932916564023 y2[1] (numeric) = 1.099932916564023 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10011 y1[1] (analytic) = 1.994993177582442 y1[1] (numeric) = 1.994993177582441 absolute error = 2.220446049250313e-16 relative error = 1.11300934469414e-14 % h = 1e-05 y2[1] (analytic) = 1.099942866500796 y2[1] (numeric) = 1.099942866500796 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10012 y1[1] (analytic) = 1.994992178104027 y1[1] (numeric) = 1.994992178104027 absolute error = 2.220446049250313e-16 relative error = 1.113009902304755e-14 % h = 1e-05 y2[1] (analytic) = 1.099952816427574 y2[1] (numeric) = 1.099952816427574 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10013 y1[1] (analytic) = 1.994991178526113 y1[1] (numeric) = 1.994991178526113 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099962766344358 y2[1] (numeric) = 1.099962766344357 absolute error = 2.220446049250313e-16 relative error = 2.018655646526833e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10014 y1[1] (analytic) = 1.9949901788487 y1[1] (numeric) = 1.9949901788487 absolute error = 2.220446049250313e-16 relative error = 1.113011017694194e-14 % h = 1e-05 y2[1] (analytic) = 1.099972716251145 y2[1] (numeric) = 1.099972716251144 absolute error = 2.220446049250313e-16 relative error = 2.01863738658709e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001499999999999 y1[1] (analytic) = 1.994989179071788 y1[1] (numeric) = 1.994989179071788 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.099982666147934 y2[1] (numeric) = 1.099982666147934 absolute error = 2.220446049250313e-16 relative error = 2.018619126996034e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001599999999999 y1[1] (analytic) = 1.994988179195377 y1[1] (numeric) = 1.994988179195377 absolute error = 2.220446049250313e-16 relative error = 1.113012133307912e-14 % h = 1e-05 y2[1] (analytic) = 1.099992616034726 y2[1] (numeric) = 1.099992616034725 absolute error = 2.220446049250313e-16 relative error = 2.018600867753658e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001699999999999 y1[1] (analytic) = 1.994987179219467 y1[1] (numeric) = 1.994987179219467 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100002565911518 y2[1] (numeric) = 1.100002565911518 absolute error = 2.220446049250313e-16 relative error = 2.018582608859952e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001799999999999 y1[1] (analytic) = 1.994986179144059 y1[1] (numeric) = 1.994986179144059 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10001251577831 y2[1] (numeric) = 1.100012515778309 absolute error = 2.220446049250313e-16 relative error = 2.01856435031491e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001899999999999 y1[1] (analytic) = 1.994985178969152 y1[1] (numeric) = 1.994985178969152 absolute error = 2.220446049250313e-16 relative error = 1.113013807149014e-14 % h = 1e-05 y2[1] (analytic) = 1.1000224656351 y2[1] (numeric) = 1.1000224656351 absolute error = 2.220446049250313e-16 relative error = 2.018546092118522e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001999999999999 y1[1] (analytic) = 1.994984178694746 y1[1] (numeric) = 1.994984178694746 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100032415481889 y2[1] (numeric) = 1.100032415481889 absolute error = 2.220446049250313e-16 relative error = 2.018527834270781e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002099999999999 y1[1] (analytic) = 1.994983178320842 y1[1] (numeric) = 1.994983178320842 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100042365318674 y2[1] (numeric) = 1.100042365318674 absolute error = 2.220446049250313e-16 relative error = 2.018509576771679e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002199999999999 y1[1] (analytic) = 1.99498217784744 y1[1] (numeric) = 1.99498217784744 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100052315145455 y2[1] (numeric) = 1.100052315145455 absolute error = 2.220446049250313e-16 relative error = 2.018491319621207e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002299999999999 y1[1] (analytic) = 1.994981177274539 y1[1] (numeric) = 1.994981177274539 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10006226496223 y2[1] (numeric) = 1.10006226496223 absolute error = 2.220446049250313e-16 relative error = 2.018473062819358e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002399999999999 y1[1] (analytic) = 1.994980176602141 y1[1] (numeric) = 1.994980176602141 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100072214769 y2[1] (numeric) = 1.100072214769 absolute error = 2.220446049250313e-16 relative error = 2.018454806366122e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002499999999999 y1[1] (analytic) = 1.994979175830244 y1[1] (numeric) = 1.994979175830244 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100082164565762 y2[1] (numeric) = 1.100082164565762 absolute error = 2.220446049250313e-16 relative error = 2.018436550261493e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002599999999999 y1[1] (analytic) = 1.99497817495885 y1[1] (numeric) = 1.994978174958849 absolute error = 2.220446049250313e-16 relative error = 1.113017714740721e-14 % h = 1e-05 y2[1] (analytic) = 1.100092114352516 y2[1] (numeric) = 1.100092114352516 absolute error = 2.220446049250313e-16 relative error = 2.018418294505462e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002699999999999 y1[1] (analytic) = 1.994977173987957 y1[1] (numeric) = 1.994977173987957 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100102064129261 y2[1] (numeric) = 1.100102064129261 absolute error = 2.220446049250313e-16 relative error = 2.01840003909802e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002799999999999 y1[1] (analytic) = 1.994976172917567 y1[1] (numeric) = 1.994976172917567 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100112013895996 y2[1] (numeric) = 1.100112013895995 absolute error = 4.440892098500626e-16 relative error = 4.036763568078321e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002899999999999 y1[1] (analytic) = 1.994975171747679 y1[1] (numeric) = 1.994975171747679 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100121963652719 y2[1] (numeric) = 1.100121963652719 absolute error = 4.440892098500626e-16 relative error = 4.036727058657748e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1002999999999999 y1[1] (analytic) = 1.994974170478294 y1[1] (numeric) = 1.994974170478294 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10013191339943 y2[1] (numeric) = 1.10013191339943 absolute error = 4.440892098500626e-16 relative error = 4.036690549934306e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003099999999999 y1[1] (analytic) = 1.994973169109411 y1[1] (numeric) = 1.994973169109411 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100141863136128 y2[1] (numeric) = 1.100141863136128 absolute error = 2.220446049250313e-16 relative error = 2.018327020953989e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003199999999999 y1[1] (analytic) = 1.994972167641031 y1[1] (numeric) = 1.994972167641031 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100151812862812 y2[1] (numeric) = 1.100151812862812 absolute error = 2.220446049250313e-16 relative error = 2.018308767289375e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003299999999999 y1[1] (analytic) = 1.994971166073154 y1[1] (numeric) = 1.994971166073154 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100161762579481 y2[1] (numeric) = 1.10016176257948 absolute error = 2.220446049250313e-16 relative error = 2.018290513973301e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003399999999999 y1[1] (analytic) = 1.99497016440578 y1[1] (numeric) = 1.99497016440578 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100171712286133 y2[1] (numeric) = 1.100171712286133 absolute error = 2.220446049250313e-16 relative error = 2.018272261005761e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003499999999999 y1[1] (analytic) = 1.994969162638908 y1[1] (numeric) = 1.994969162638908 absolute error = 2.220446049250313e-16 relative error = 1.113022742824329e-14 % h = 1e-05 y2[1] (analytic) = 1.100181661982768 y2[1] (numeric) = 1.100181661982768 absolute error = 2.220446049250313e-16 relative error = 2.018254008386745e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003599999999999 y1[1] (analytic) = 1.99496816077254 y1[1] (numeric) = 1.99496816077254 absolute error = 2.220446049250313e-16 relative error = 1.113023301780645e-14 % h = 1e-05 y2[1] (analytic) = 1.100191611669386 y2[1] (numeric) = 1.100191611669385 absolute error = 4.440892098500626e-16 relative error = 4.03647151223249e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003699999999999 y1[1] (analytic) = 1.994967158806675 y1[1] (numeric) = 1.994967158806675 absolute error = 2.220446049250313e-16 relative error = 1.113023860793033e-14 % h = 1e-05 y2[1] (analytic) = 1.100201561345984 y2[1] (numeric) = 1.100201561345983 absolute error = 4.440892098500626e-16 relative error = 4.036435008388509e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003799999999999 y1[1] (analytic) = 1.994966156741313 y1[1] (numeric) = 1.994966156741313 absolute error = 2.220446049250313e-16 relative error = 1.113024419861493e-14 % h = 1e-05 y2[1] (analytic) = 1.100211511012561 y2[1] (numeric) = 1.100211511012561 absolute error = 4.440892098500626e-16 relative error = 4.036398505241528e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003899999999999 y1[1] (analytic) = 1.994965154576455 y1[1] (numeric) = 1.994965154576454 absolute error = 2.220446049250313e-16 relative error = 1.113024978986026e-14 % h = 1e-05 y2[1] (analytic) = 1.100221460669118 y2[1] (numeric) = 1.100221460669118 absolute error = 4.440892098500626e-16 relative error = 4.036362002791532e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1003999999999999 y1[1] (analytic) = 1.9949641523121 y1[1] (numeric) = 1.9949641523121 absolute error = 2.220446049250313e-16 relative error = 1.113025538166632e-14 % h = 1e-05 y2[1] (analytic) = 1.100231410315653 y2[1] (numeric) = 1.100231410315652 absolute error = 4.440892098500626e-16 relative error = 4.036325501038504e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004099999999998 y1[1] (analytic) = 1.994963149948249 y1[1] (numeric) = 1.994963149948248 absolute error = 2.220446049250313e-16 relative error = 1.11302609740331e-14 % h = 1e-05 y2[1] (analytic) = 1.100241359952164 y2[1] (numeric) = 1.100241359952163 absolute error = 6.661338147750939e-16 relative error = 6.05443349997364e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004199999999998 y1[1] (analytic) = 1.994962147484901 y1[1] (numeric) = 1.994962147484901 absolute error = 2.220446049250313e-16 relative error = 1.113026656696061e-14 % h = 1e-05 y2[1] (analytic) = 1.100251309578651 y2[1] (numeric) = 1.100251309578651 absolute error = 6.661338147750939e-16 relative error = 6.054378749434931e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004299999999998 y1[1] (analytic) = 1.994961144922057 y1[1] (numeric) = 1.994961144922057 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100261259195113 y2[1] (numeric) = 1.100261259195113 absolute error = 6.661338147750939e-16 relative error = 6.054323999941599e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004399999999998 y1[1] (analytic) = 1.994960142259717 y1[1] (numeric) = 1.994960142259717 absolute error = 2.220446049250313e-16 relative error = 1.113027775449782e-14 % h = 1e-05 y2[1] (analytic) = 1.100271208801549 y2[1] (numeric) = 1.100271208801549 absolute error = 6.661338147750939e-16 relative error = 6.054269251493622e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004499999999998 y1[1] (analytic) = 1.994959139497881 y1[1] (numeric) = 1.994959139497881 absolute error = 2.220446049250313e-16 relative error = 1.113028334910752e-14 % h = 1e-05 y2[1] (analytic) = 1.100281158397958 y2[1] (numeric) = 1.100281158397957 absolute error = 6.661338147750939e-16 relative error = 6.054214504090977e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004599999999998 y1[1] (analytic) = 1.994958136636549 y1[1] (numeric) = 1.994958136636549 absolute error = 2.220446049250313e-16 relative error = 1.113028894427796e-14 % h = 1e-05 y2[1] (analytic) = 1.100291107984339 y2[1] (numeric) = 1.100291107984338 absolute error = 6.661338147750939e-16 relative error = 6.054159757733636e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004699999999998 y1[1] (analytic) = 1.994957133675721 y1[1] (numeric) = 1.994957133675721 absolute error = 2.220446049250313e-16 relative error = 1.113029454000912e-14 % h = 1e-05 y2[1] (analytic) = 1.100301057560691 y2[1] (numeric) = 1.10030105756069 absolute error = 6.661338147750939e-16 relative error = 6.054105012421577e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004799999999998 y1[1] (analytic) = 1.994956130615398 y1[1] (numeric) = 1.994956130615398 absolute error = 2.220446049250313e-16 relative error = 1.113030013630103e-14 % h = 1e-05 y2[1] (analytic) = 1.100311007127012 y2[1] (numeric) = 1.100311007127011 absolute error = 6.661338147750939e-16 relative error = 6.054050268154776e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004899999999998 y1[1] (analytic) = 1.994955127455579 y1[1] (numeric) = 1.994955127455579 absolute error = 2.220446049250313e-16 relative error = 1.113030573315367e-14 % h = 1e-05 y2[1] (analytic) = 1.100320956683303 y2[1] (numeric) = 1.100320956683302 absolute error = 6.661338147750939e-16 relative error = 6.053995524933207e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1004999999999998 y1[1] (analytic) = 1.994954124196264 y1[1] (numeric) = 1.994954124196264 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100330906229561 y2[1] (numeric) = 1.10033090622956 absolute error = 6.661338147750939e-16 relative error = 6.053940782756847e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005099999999998 y1[1] (analytic) = 1.994953120837454 y1[1] (numeric) = 1.994953120837454 absolute error = 2.220446049250313e-16 relative error = 1.113031692854116e-14 % h = 1e-05 y2[1] (analytic) = 1.100340855765786 y2[1] (numeric) = 1.100340855765786 absolute error = 4.440892098500626e-16 relative error = 4.035924027750448e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005199999999998 y1[1] (analytic) = 1.994952117379149 y1[1] (numeric) = 1.994952117379149 absolute error = 2.220446049250313e-16 relative error = 1.113032252707601e-14 % h = 1e-05 y2[1] (analytic) = 1.100350805291977 y2[1] (numeric) = 1.100350805291977 absolute error = 4.440892098500626e-16 relative error = 4.035887534359771e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005299999999998 y1[1] (analytic) = 1.994951113821348 y1[1] (numeric) = 1.994951113821348 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100360754808133 y2[1] (numeric) = 1.100360754808133 absolute error = 4.440892098500626e-16 relative error = 4.03585104166585e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005399999999998 y1[1] (analytic) = 1.994950110164053 y1[1] (numeric) = 1.994950110164053 absolute error = 2.220446049250313e-16 relative error = 1.113033372582795e-14 % h = 1e-05 y2[1] (analytic) = 1.100370704314253 y2[1] (numeric) = 1.100370704314253 absolute error = 4.440892098500626e-16 relative error = 4.03581454966867e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005499999999998 y1[1] (analytic) = 1.994949106407262 y1[1] (numeric) = 1.994949106407262 absolute error = 2.220446049250313e-16 relative error = 1.113033932604502e-14 % h = 1e-05 y2[1] (analytic) = 1.100380653810336 y2[1] (numeric) = 1.100380653810336 absolute error = 2.220446049250313e-16 relative error = 2.017889029184108e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005599999999998 y1[1] (analytic) = 1.994948102550977 y1[1] (numeric) = 1.994948102550976 absolute error = 2.220446049250313e-16 relative error = 1.113034492682285e-14 % h = 1e-05 y2[1] (analytic) = 1.100390603296381 y2[1] (numeric) = 1.100390603296381 absolute error = 4.440892098500626e-16 relative error = 4.035741567764468e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005699999999998 y1[1] (analytic) = 1.994947098595196 y1[1] (numeric) = 1.994947098595196 absolute error = 2.220446049250313e-16 relative error = 1.113035052816142e-14 % h = 1e-05 y2[1] (analytic) = 1.100400552772387 y2[1] (numeric) = 1.100400552772387 absolute error = 4.440892098500626e-16 relative error = 4.035705077857413e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005799999999998 y1[1] (analytic) = 1.994946094539921 y1[1] (numeric) = 1.994946094539921 absolute error = 2.220446049250313e-16 relative error = 1.113035613006073e-14 % h = 1e-05 y2[1] (analytic) = 1.100410502238353 y2[1] (numeric) = 1.100410502238352 absolute error = 4.440892098500626e-16 relative error = 4.035668588647033e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005899999999998 y1[1] (analytic) = 1.994945090385152 y1[1] (numeric) = 1.994945090385151 absolute error = 4.440892098500626e-16 relative error = 2.226072346504159e-14 % h = 1e-05 y2[1] (analytic) = 1.100420451694277 y2[1] (numeric) = 1.100420451694277 absolute error = 4.440892098500626e-16 relative error = 4.035632100133313e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1005999999999998 y1[1] (analytic) = 1.994944086130887 y1[1] (numeric) = 1.994944086130887 absolute error = 4.440892098500626e-16 relative error = 2.226073467108321e-14 % h = 1e-05 y2[1] (analytic) = 1.10043040114016 y2[1] (numeric) = 1.10043040114016 absolute error = 4.440892098500626e-16 relative error = 4.035595612316236e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006099999999998 y1[1] (analytic) = 1.994943081777129 y1[1] (numeric) = 1.994943081777128 absolute error = 4.440892098500626e-16 relative error = 2.226074587824634e-14 % h = 1e-05 y2[1] (analytic) = 1.100440350576 y2[1] (numeric) = 1.100440350575999 absolute error = 2.220446049250313e-16 relative error = 2.017779562597893e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006199999999998 y1[1] (analytic) = 1.994942077323876 y1[1] (numeric) = 1.994942077323876 absolute error = 2.220446049250313e-16 relative error = 1.113037854326548e-14 % h = 1e-05 y2[1] (analytic) = 1.100450300001795 y2[1] (numeric) = 1.100450300001795 absolute error = 2.220446049250313e-16 relative error = 2.017761319385974e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006299999999998 y1[1] (analytic) = 1.994941072771129 y1[1] (numeric) = 1.994941072771128 absolute error = 4.440892098500626e-16 relative error = 2.226076829593709e-14 % h = 1e-05 y2[1] (analytic) = 1.100460249417546 y2[1] (numeric) = 1.100460249417546 absolute error = 2.220446049250313e-16 relative error = 2.017743076522351e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006399999999998 y1[1] (analytic) = 1.994940068118888 y1[1] (numeric) = 1.994940068118887 absolute error = 4.440892098500626e-16 relative error = 2.226077950646472e-14 % h = 1e-05 y2[1] (analytic) = 1.10047019882325 y2[1] (numeric) = 1.10047019882325 absolute error = 2.220446049250313e-16 relative error = 2.017724834007018e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006499999999998 y1[1] (analytic) = 1.994939063367152 y1[1] (numeric) = 1.994939063367152 absolute error = 2.220446049250313e-16 relative error = 1.113039535905693e-14 % h = 1e-05 y2[1] (analytic) = 1.100480148218908 y2[1] (numeric) = 1.100480148218908 absolute error = 2.220446049250313e-16 relative error = 2.017706591839966e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006599999999997 y1[1] (analytic) = 1.994938058515923 y1[1] (numeric) = 1.994938058515923 absolute error = 2.220446049250313e-16 relative error = 1.113040096544226e-14 % h = 1e-05 y2[1] (analytic) = 1.100490097604517 y2[1] (numeric) = 1.100490097604517 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006699999999997 y1[1] (analytic) = 1.9949370535652 y1[1] (numeric) = 1.9949370535652 absolute error = 2.220446049250313e-16 relative error = 1.113040657238834e-14 % h = 1e-05 y2[1] (analytic) = 1.100500046980078 y2[1] (numeric) = 1.100500046980078 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006799999999997 y1[1] (analytic) = 1.994936048514984 y1[1] (numeric) = 1.994936048514983 absolute error = 2.220446049250313e-16 relative error = 1.113041217989518e-14 % h = 1e-05 y2[1] (analytic) = 1.100509996345588 y2[1] (numeric) = 1.100509996345588 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006899999999997 y1[1] (analytic) = 1.994935043365273 y1[1] (numeric) = 1.994935043365273 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100519945701048 y2[1] (numeric) = 1.100519945701048 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1006999999999997 y1[1] (analytic) = 1.99493403811607 y1[1] (numeric) = 1.99493403811607 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100529895046455 y2[1] (numeric) = 1.100529895046455 absolute error = 2.220446049250313e-16 relative error = 2.017615386228635e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007099999999997 y1[1] (analytic) = 1.994933032767372 y1[1] (numeric) = 1.994933032767372 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10053984438181 y2[1] (numeric) = 1.10053984438181 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007199999999997 y1[1] (analytic) = 1.994932027319182 y1[1] (numeric) = 1.994932027319182 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10054979370711 y2[1] (numeric) = 1.10054979370711 absolute error = 2.220446049250313e-16 relative error = 2.017578906421785e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007299999999997 y1[1] (analytic) = 1.994931021771498 y1[1] (numeric) = 1.994931021771498 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100559743022356 y2[1] (numeric) = 1.100559743022356 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007399999999997 y1[1] (analytic) = 1.994930016124322 y1[1] (numeric) = 1.994930016124322 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100569692327545 y2[1] (numeric) = 1.100569692327545 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007499999999997 y1[1] (analytic) = 1.994929010377652 y1[1] (numeric) = 1.994929010377652 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100579641622678 y2[1] (numeric) = 1.100579641622678 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007599999999997 y1[1] (analytic) = 1.994928004531489 y1[1] (numeric) = 1.994928004531489 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100589590907753 y2[1] (numeric) = 1.100589590907753 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007699999999997 y1[1] (analytic) = 1.994926998585834 y1[1] (numeric) = 1.994926998585834 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100599540182768 y2[1] (numeric) = 1.100599540182768 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007799999999997 y1[1] (analytic) = 1.994925992540685 y1[1] (numeric) = 1.994925992540686 absolute error = 2.220446049250313e-16 relative error = 1.113046828580549e-14 % h = 1e-05 y2[1] (analytic) = 1.100609489447724 y2[1] (numeric) = 1.100609489447724 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007899999999997 y1[1] (analytic) = 1.994924986396045 y1[1] (numeric) = 1.994924986396045 absolute error = 2.220446049250313e-16 relative error = 1.113047389948073e-14 % h = 1e-05 y2[1] (analytic) = 1.100619438702619 y2[1] (numeric) = 1.100619438702619 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1007999999999997 y1[1] (analytic) = 1.994923980151912 y1[1] (numeric) = 1.994923980151912 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100629387947452 y2[1] (numeric) = 1.100629387947452 absolute error = 2.220446049250313e-16 relative error = 2.017433001122378e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008099999999997 y1[1] (analytic) = 1.994922973808286 y1[1] (numeric) = 1.994922973808286 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100639337182221 y2[1] (numeric) = 1.100639337182222 absolute error = 2.220446049250313e-16 relative error = 2.017414764526717e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008199999999997 y1[1] (analytic) = 1.994921967365168 y1[1] (numeric) = 1.994921967365168 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100649286406927 y2[1] (numeric) = 1.100649286406927 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008299999999997 y1[1] (analytic) = 1.994920960822558 y1[1] (numeric) = 1.994920960822558 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100659235621569 y2[1] (numeric) = 1.100659235621569 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008399999999997 y1[1] (analytic) = 1.994919954180456 y1[1] (numeric) = 1.994919954180455 absolute error = 2.220446049250313e-16 relative error = 1.113050197626855e-14 % h = 1e-05 y2[1] (analytic) = 1.100669184826144 y2[1] (numeric) = 1.100669184826144 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008499999999997 y1[1] (analytic) = 1.994918947438861 y1[1] (numeric) = 1.994918947438861 absolute error = 2.220446049250313e-16 relative error = 1.113050759330844e-14 % h = 1e-05 y2[1] (analytic) = 1.100679134020652 y2[1] (numeric) = 1.100679134020652 absolute error = 2.220446049250313e-16 relative error = 2.017341821625422e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008599999999997 y1[1] (analytic) = 1.994917940597775 y1[1] (numeric) = 1.994917940597775 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100689083205092 y2[1] (numeric) = 1.100689083205092 absolute error = 2.220446049250313e-16 relative error = 2.017323586770394e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008699999999997 y1[1] (analytic) = 1.994916933657197 y1[1] (numeric) = 1.994916933657197 absolute error = 2.220446049250313e-16 relative error = 1.113051882907056e-14 % h = 1e-05 y2[1] (analytic) = 1.100699032379463 y2[1] (numeric) = 1.100699032379463 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008799999999997 y1[1] (analytic) = 1.994915926617128 y1[1] (numeric) = 1.994915926617127 absolute error = 2.220446049250313e-16 relative error = 1.113052444779278e-14 % h = 1e-05 y2[1] (analytic) = 1.100708981543765 y2[1] (numeric) = 1.100708981543765 absolute error = 2.220446049250313e-16 relative error = 2.017287118104639e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008899999999997 y1[1] (analytic) = 1.994914919477566 y1[1] (numeric) = 1.994914919477566 absolute error = 2.220446049250313e-16 relative error = 1.113053006707579e-14 % h = 1e-05 y2[1] (analytic) = 1.100718930697995 y2[1] (numeric) = 1.100718930697995 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1008999999999997 y1[1] (analytic) = 1.994913912238514 y1[1] (numeric) = 1.994913912238514 absolute error = 2.220446049250313e-16 relative error = 1.113053568691958e-14 % h = 1e-05 y2[1] (analytic) = 1.100728879842154 y2[1] (numeric) = 1.100728879842154 absolute error = 2.220446049250313e-16 relative error = 2.017250650831228e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009099999999997 y1[1] (analytic) = 1.99491290489997 y1[1] (numeric) = 1.994912904899969 absolute error = 2.220446049250313e-16 relative error = 1.113054130732415e-14 % h = 1e-05 y2[1] (analytic) = 1.10073882897624 y2[1] (numeric) = 1.10073882897624 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009199999999996 y1[1] (analytic) = 1.994911897461934 y1[1] (numeric) = 1.994911897461934 absolute error = 2.220446049250313e-16 relative error = 1.113054692828951e-14 % h = 1e-05 y2[1] (analytic) = 1.100748778100252 y2[1] (numeric) = 1.100748778100252 absolute error = 2.220446049250313e-16 relative error = 2.017214184950096e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009299999999996 y1[1] (analytic) = 1.994910889924408 y1[1] (numeric) = 1.994910889924407 absolute error = 2.220446049250313e-16 relative error = 1.113055254981565e-14 % h = 1e-05 y2[1] (analytic) = 1.100758727214189 y2[1] (numeric) = 1.100758727214189 absolute error = 0 relative error = 0 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009399999999996 y1[1] (analytic) = 1.99490988228739 y1[1] (numeric) = 1.99490988228739 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.10076867631805 y2[1] (numeric) = 1.10076867631805 absolute error = 2.220446049250313e-16 relative error = 2.017177720461179e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009499999999996 y1[1] (analytic) = 1.994908874550881 y1[1] (numeric) = 1.994908874550881 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100778625411834 y2[1] (numeric) = 1.100778625411834 absolute error = 2.220446049250313e-16 relative error = 2.017159488738781e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009599999999996 y1[1] (analytic) = 1.994907866714882 y1[1] (numeric) = 1.994907866714882 absolute error = 0 relative error = 0 % h = 1e-05 y2[1] (analytic) = 1.100788574495541 y2[1] (numeric) = 1.100788574495541 absolute error = 2.220446049250313e-16 relative error = 2.017141257364412e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009699999999996 y1[1] (analytic) = 1.994906858779391 y1[1] (numeric) = 1.994906858779391 absolute error = 2.220446049250313e-16 relative error = 1.113057504152811e-14 % h = 1e-05 y2[1] (analytic) = 1.100798523569168 y2[1] (numeric) = 1.100798523569168 absolute error = 4.440892098500626e-16 relative error = 4.034246052676128e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009799999999996 y1[1] (analytic) = 1.99490585074441 y1[1] (numeric) = 1.99490585074441 absolute error = 2.220446049250313e-16 relative error = 1.11305806658582e-14 % h = 1e-05 y2[1] (analytic) = 1.100808472632716 y2[1] (numeric) = 1.100808472632716 absolute error = 2.220446049250313e-16 relative error = 2.017104795659729e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009899999999996 y1[1] (analytic) = 1.994904842609939 y1[1] (numeric) = 1.994904842609939 absolute error = 2.220446049250313e-16 relative error = 1.113058629074908e-14 % h = 1e-05 y2[1] (analytic) = 1.100818421686183 y2[1] (numeric) = 1.100818421686183 absolute error = 2.220446049250313e-16 relative error = 2.0170865653294e-14 % h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1009999999999996 y1[1] (analytic) = 1.994903834375977 y1[1] (numeric) = 1.994903834375976 absolute error = 2.220446049250313e-16 relative error = 1.113059191620075e-14 % h = 1e-05 y2[1] (analytic) = 1.100828370729568 y2[1] (numeric) = 1.100828370729568 absolute error = 2.220446049250313e-16 relative error = 2.017068335347067e-14 % h = 1e-05 Finished! Maximum Iterations Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 100 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Time to Timeout = 1 Minutes 0 Seconds Percent Done = 0.0102 %