Initializing... Initialized Initializing(2)... PI = 0.314159265358979323846264338327950271e1+/-0.313e-33 E = 0.271828182845904523536028747135266232e1+/-0.256e-32 LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(2.0) x_end=c(3.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.0001) $glob_upper_ratio_limit=c(1.001) $glob_lower_ratio_limit=c(0.999) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(-1.5) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb #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 def exact_soln_y (x) x = c(x) return(sin(sqrt(c(2.0)*c(x)+c(3.0)))-sqrt(c(2.0)*c(x)+c(3.0))*cos(sqrt(c(2.0)*c(x)+c(3.0)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.2e1+/-0.50e-33 y[1] (closed_form) 0.28028919695910200650978160660307081e1+/-0.112e-29 y[1] (numeric) 0.28028919695910200650978160660307081e1+/-0.112e-29 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.224e-29 relative error 0.0e0+/-0.799174575510609624340180903556765638e-28% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.201e1+/-0.550e-32 y[1] (closed_form) 0.280763306229678183753524357524299208e1+/-0.487e-29 y[1] (numeric) 0.280763472509488161351757588072784632e1+/-0.112e-29 absolute error 0.166279809977598233230548485424e-5+/-0.599e-29 relative error 0.592241957150815057611255958646551033e-4+/-0.213e-27% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.202e1+/-0.105e-31 y[1] (closed_form) 0.281234089028137634540763403034859158e1+/-0.87e-29 y[1] (numeric) 0.28123442168735966008542644483594779e1+/-0.112e-29 absolute error 0.332659222025544663041801088632e-5+/-0.982e-29 relative error 0.11828552618749639342922769329591793e-3+/-0.349e-27% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.203e1+/-0.155e-31 y[1] (closed_form) 0.281701543390901901354767149807499586e1+/-0.125e-28 y[1] (numeric) 0.281702042526352109519012853241825602e1+/-0.112e-29 absolute error 0.499135450208164245703434326016e-5+/-0.136e-28 relative error 0.177185912508665650004716551639957966e-3+/-0.482e-27% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.204e1+/-0.205e-31 y[1] (closed_form) 0.28216566740992080296305186513018473e1+/-0.164e-28 y[1] (numeric) 0.282166333115647740392705809144953405e1+/-0.112e-29 absolute error 0.665705726937429653944014768675e-5+/-0.175e-28 relative error 0.235927259701058788477164341031023803e-3+/-0.62e-27% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.205e1+/-0.255e-31 y[1] (closed_form) 0.282626459232306976099477364240747217e1+/-0.203e-28 y[1] (numeric) 0.282627291599609806832352415354065342e1+/-0.112e-29 absolute error 0.832367302830732875051113318125e-5+/-0.214e-28 relative error 0.294511456956888178374004442547655878e-3+/-0.757e-27% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.206e1+/-0.305e-31 y[1] (closed_form) 0.283083917059973245321906840479919295e1+/-0.241e-28 y[1] (numeric) 0.283084916177419815524302048506883475e1+/-0.112e-29 absolute error 0.99911744657020239520802696418e-5+/-0.252e-28 relative error 0.35294037787336841059252642683783754e-3+/-0.89e-27% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.207e1+/-0.355e-31 y[1] (closed_form) 0.283538039149272790367376873905228102e1+/-0.277e-28 y[1] (numeric) 0.283539205102717553911456850438238562e1+/-0.112e-29 absolute error 0.116595344476354407997653301046e-4+/-0.288e-28 relative error 0.411215880684605659011713414331109197e-3+/-0.101e-26% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.208e1+/-0.405e-31 y[1] (closed_form) 0.283988823810642080760481742886030916e1+/-0.315e-28 y[1] (numeric) 0.283990156683243887144719584432561706e1+/-0.112e-29 absolute error 0.133287260180638423784154653079e-4+/-0.326e-28 relative error 0.469339808490180702801632981934693327e-3+/-0.114e-26% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.209e1+/-0.455e-31 y[1] (closed_form) 0.284436269408246547856975874433918309e1+/-0.357e-28 y[1] (numeric) 0.284437769280486293950699020954290081e1+/-0.112e-29 absolute error 0.1499872239746093723146520371772e-4+/-0.368e-28 relative error 0.527313989480488005109338281961907889e-3+/-0.129e-26% Desired digits 8 Estimated correct digits 13 Correct digits 4 h 0.1e-2+/-0.5e-33 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations 95 Total Elapsed Time 3 Minutes 2 Seconds Elapsed Time(since restart) 3 Minutes 1 Seconds Expected Time Remaining 28 Minutes 33 Seconds Optimized Time Remaining 28 Minutes 24 Seconds Expected Total Time 31 Minutes 26 Seconds Time to Timeout 0.0 Seconds Percent Done 0.96e1+/-0.49e-29%