##############ECHO OF PROBLEM################# ##############temp/arcsin_sqrtpostode.ode################# diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=c(0.01); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.5); array_given_ord_poles[1][2]=c(0.0); // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=false; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arcsin(sqrt ( c(0.1) * c(x) + c(0.2))) + c(5.0) * sqrt( c(0.1) * c(x) + c(0.2)) * sqrt( c(0.8) - c(0.1) * c(x)) - c(5.0) * arcsin(sqrt( c(0.1) * c(x) + c(0.2)))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 0.609057172997582 y[1] (numeric) = 0.609057172997582 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.01 y[1] (closed_form) = 0.6136998951900665 y[1] (numeric) = 0.613699895177051 absolute error = 1.30154775845881e-11 relative error = 2.120821216786607e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.02000000000000001 y[1] (closed_form) = 0.6183550940668945 y[1] (numeric) = 0.6183550940408706 absolute error = 2.602384974181859e-11 relative error = 4.208560743093563e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.03000000000000002 y[1] (closed_form) = 0.6230227465023472 y[1] (numeric) = 0.6230227464633225 absolute error = 3.90247834047841e-11 relative error = 6.263781478905775e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.04000000000000003 y[1] (closed_form) = 0.627702829575655 y[1] (numeric) = 0.6277028295236377 absolute error = 5.201739039506492e-11 relative error = 8.286945341672293e-09 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 11 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 0.6323953205685546 y[1] (numeric) = 0.6323953205035511 absolute error = 6.500355809180292e-11 relative error = 1.027894356228973e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.06000000000000005 y[1] (closed_form) = 0.6371001969628827 y[1] (numeric) = 0.6371001968849014 absolute error = 7.798128809355376e-11 relative error = 1.224003515699697e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.07000000000000005 y[1] (closed_form) = 0.6418174364382216 y[1] (numeric) = 0.6418174363472684 absolute error = 9.095324493557655e-11 relative error = 1.417120192937159e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.08000000000000006 y[1] (closed_form) = 0.6465470168695724 y[1] (numeric) = 0.6465470167656547 absolute error = 1.039176522610319e-10 relative error = 1.60727139016396e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.09000000000000007 y[1] (closed_form) = 0.6512889163250812 y[1] (numeric) = 0.6512889162082056 absolute error = 1.168756202929444e-10 relative error = 1.794528009971655e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 0.6560431130637943 y[1] (numeric) = 0.6560431129339668 absolute error = 1.298274820982215e-10 relative error = 1.978947412341739e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1100000000000001 y[1] (closed_form) = 0.660809585533455 y[1] (numeric) = 0.6608095853906816 absolute error = 1.42773459721468e-10 relative error = 2.160583969226333e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1200000000000001 y[1] (closed_form) = 0.665588312368337 y[1] (numeric) = 0.6655883122126249 absolute error = 1.557121098727521e-10 relative error = 2.339465807605421e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1300000000000001 y[1] (closed_form) = 0.6703792723871183 y[1] (numeric) = 0.6703792722184735 absolute error = 1.686447648197031e-10 relative error = 2.515661980705115e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1400000000000001 y[1] (closed_form) = 0.675182444590785 y[1] (numeric) = 0.6751824444092118 absolute error = 1.815732009191606e-10 relative error = 2.689246475139155e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 0.6799978081605684 y[1] (numeric) = 0.6799978079660729 absolute error = 1.944955307919827e-10 relative error = 2.860237613384429e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1600000000000001 y[1] (closed_form) = 0.6848253424559259 y[1] (numeric) = 0.6848253422485134 absolute error = 2.074124205719841e-10 relative error = 3.028690787466481e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1700000000000001 y[1] (closed_form) = 0.6896650270125453 y[1] (numeric) = 0.6896650267922213 absolute error = 2.203239812814672e-10 relative error = 3.194652079660398e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1800000000000001 y[1] (closed_form) = 0.6945168415403891 y[1] (numeric) = 0.6945168413071584 absolute error = 2.332306570096421e-10 relative error = 3.358171365468302e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (closed_form) = 0.6993807659217648 y[1] (numeric) = 0.6993807656756319 absolute error = 2.461328918457184e-10 relative error = 3.519297410493152e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 0.7042567802094295 y[1] (numeric) = 0.7042567799504005 absolute error = 2.590290204551593e-10 relative error = 3.678047946916892e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2100000000000002 y[1] (closed_form) = 0.7091448646247316 y[1] (numeric) = 0.709144864352809 absolute error = 2.719225955516436e-10 relative error = 3.834514062166138e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2200000000000002 y[1] (closed_form) = 0.7140449995557643 y[1] (numeric) = 0.7140449992709537 absolute error = 2.848106195330047e-10 relative error = 3.988692865438406e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2300000000000002 y[1] (closed_form) = 0.7189571655555724 y[1] (numeric) = 0.7189571652578782 absolute error = 2.976942026222673e-10 relative error = 4.140638926551693e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2400000000000002 y[1] (closed_form) = 0.7238813433403708 y[1] (numeric) = 0.7238813430297969 absolute error = 3.105738999309438e-10 relative error = 4.290397905515726e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 0.7288175137877979 y[1] (numeric) = 0.7288175134643475 absolute error = 3.234503775928488e-10 relative error = 4.438015984437833e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2600000000000002 y[1] (closed_form) = 0.7337656579351934 y[1] (numeric) = 0.7337656575988706 absolute error = 3.363228584518652e-10 relative error = 4.583518659053534e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2700000000000002 y[1] (closed_form) = 0.7387257569779107 y[1] (numeric) = 0.7387257566287182 absolute error = 3.491924527310175e-10 relative error = 4.726956511703965e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2800000000000002 y[1] (closed_form) = 0.7436977922676444 y[1] (numeric) = 0.743697791905587 absolute error = 3.620573840734664e-10 relative error = 4.868340175778928e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.2900000000000002 y[1] (closed_form) = 0.7486817453107992 y[1] (numeric) = 0.7486817449358788 absolute error = 3.749204280367735e-10 relative error = 5.007741011250826e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 0.7536775977668664 y[1] (numeric) = 0.7536775973790861 absolute error = 3.877802523533092e-10 relative error = 5.145174189896254e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (closed_form) = 0.7586853314468405 y[1] (numeric) = 0.7586853310462041 absolute error = 4.006364129338635e-10 relative error = 5.280666388657276e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (closed_form) = 0.7637049283116548 y[1] (numeric) = 0.7637049278981651 absolute error = 4.134896869345539e-10 relative error = 5.414259769786583e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (closed_form) = 0.7687363704706405 y[1] (numeric) = 0.7687363700442998 absolute error = 4.263406294668926e-10 relative error = 5.545992694555035e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (closed_form) = 0.7737796401800079 y[1] (numeric) = 0.7737796397408191 absolute error = 4.391887964416696e-10 relative error = 5.675889796473569e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 0.7788347198413588 y[1] (numeric) = 0.7788347193893231 absolute error = 4.520356311488172e-10 relative error = 5.803999483239429e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3600000000000003 y[1] (closed_form) = 0.783901592000209 y[1] (numeric) = 0.7839015915353297 absolute error = 4.648793572314958e-10 relative error = 5.930328015348281e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3700000000000003 y[1] (closed_form) = 0.7889802393445478 y[1] (numeric) = 0.7889802388668261 absolute error = 4.777216400242423e-10 relative error = 6.054925284581446e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3800000000000003 y[1] (closed_form) = 0.7940706447034058 y[1] (numeric) = 0.7940706442128441 absolute error = 4.905617023709397e-10 relative error = 6.177809312597998e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.3900000000000003 y[1] (closed_form) = 0.7991727910454558 y[1] (numeric) = 0.799172790542055 absolute error = 5.034007655169148e-10 relative error = 6.299022829072794e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 0.8042866614776245 y[1] (numeric) = 0.8042866609613865 absolute error = 5.162380523060506e-10 relative error = 6.418582789345594e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (closed_form) = 0.8094122392437333 y[1] (numeric) = 0.8094122387146597 absolute error = 5.290735627383469e-10 relative error = 6.536515474891779e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (closed_form) = 0.8145495077231564 y[1] (numeric) = 0.8145495071812481 absolute error = 5.419082960145261e-10 relative error = 6.65285892234197e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (closed_form) = 0.8196984504294957 y[1] (numeric) = 0.819698449874754 absolute error = 5.547416970230756e-10 relative error = 6.76763139825882e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (closed_form) = 0.8248590510092804 y[1] (numeric) = 0.8248590504417072 absolute error = 5.675732106524833e-10 relative error = 6.880850855161407e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 0.8300312932406859 y[1] (numeric) = 0.8300312926602806 absolute error = 5.804052793934034e-10 relative error = 6.992571052680806e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4600000000000004 y[1] (closed_form) = 0.8352151610322625 y[1] (numeric) = 0.8352151604390268 absolute error = 5.932356827997864e-10 relative error = 7.102788724124599e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4700000000000004 y[1] (closed_form) = 0.8404106384216976 y[1] (numeric) = 0.840410637815631 absolute error = 6.060666413176818e-10 relative error = 7.211553657339263e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4800000000000004 y[1] (closed_form) = 0.8456177095745812 y[1] (numeric) = 0.845617708955685 absolute error = 6.188961565456452e-10 relative error = 7.318864654064584e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 TOP MAIN SOLVE Loop x[1] = 0.4900000000000004 y[1] (closed_form) = 0.850836358783202 y[1] (numeric) = 0.8508363581514757 absolute error = 6.317262268851209e-10 relative error = 7.424767646137798e-08 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Finished! diff ( y , x , 1 ) = arcsin ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %