##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 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 = 5.0; glob_h = 0.00001; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); glob_max_iter = 20; // 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_y2 (double x) { return(1.0 + cos(x)); } double exact_soln_y2p (double x) { return( -sin(x)); } double exact_soln_y2pp (double x) { return( -cos(x)); } double exact_soln_y1 (double x) { return( 1.0 - sin(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 x[1] = 0.1 y2[1] (analytic) = 1.995004165278026 y2[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 y1[1] (analytic) = 0.9001665833531718 y1[1] (numeric) = 0.9001665833531718 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10001 y2[1] (analytic) = 1.995003166894109 y2[1] (numeric) = 1.995003166894109 absolute error = 2.220446049250313e-16 relative error = 1.113003771671792e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 0.9001566333165109 y1[1] (numeric) = 0.9001566333165109 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10002 y2[1] (analytic) = 1.995002168410692 y2[1] (numeric) = 1.995002168410691 absolute error = 1.554312234475219e-15 relative error = 7.791030301052022e-14 % Correct digits = 15 h = 1e-05 y1[1] (analytic) = 0.9001466832898343 y1[1] (numeric) = 0.9001466832898343 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10003 y2[1] (analytic) = 1.995001169827775 y2[1] (numeric) = 1.99500116982777 absolute error = 4.884981308350689e-15 relative error = 2.448610748820965e-13 % Correct digits = 14 h = 1e-05 y1[1] (analytic) = 0.900136733273143 y1[1] (numeric) = 0.900136733273143 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10004 y2[1] (analytic) = 1.995000171145358 y2[1] (numeric) = 1.995000171145346 absolute error = 1.154631945610163e-14 relative error = 5.787628303546824e-13 % Correct digits = 14 h = 1e-05 y1[1] (analytic) = 0.9001267832664381 y1[1] (numeric) = 0.9001267832664381 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10005 y2[1] (analytic) = 1.99499917236344 y2[1] (numeric) = 1.994999172363418 absolute error = 2.287059430727822e-14 relative error = 1.146396180214142e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.9001168332697205 y1[1] (numeric) = 0.9001168332697205 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10006 y2[1] (analytic) = 1.994998173482023 y2[1] (numeric) = 1.994998173481984 absolute error = 3.930189507173054e-14 relative error = 1.970021606743325e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.9001068832829912 y1[1] (numeric) = 0.9001068832829912 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10007 y2[1] (analytic) = 1.994997174501106 y2[1] (numeric) = 1.994997174501044 absolute error = 6.23945339839338e-14 relative error = 3.127549992622769e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.9000969333062512 y1[1] (numeric) = 0.9000969333062512 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10008 y2[1] (analytic) = 1.994996175420689 y2[1] (numeric) = 1.994996175420596 absolute error = 9.348077867343818e-14 relative error = 4.685762299956574e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.9000869833395014 y1[1] (numeric) = 0.9000869833395014 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10009 y2[1] (analytic) = 1.994995176240773 y2[1] (numeric) = 1.99499517624064 absolute error = 1.327826737451687e-13 relative error = 6.655789213253887e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.900077033382743 y1[1] (numeric) = 0.900077033382743 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001 y2[1] (analytic) = 1.994994176961357 y2[1] (numeric) = 1.994994176961175 absolute error = 1.822986206434507e-13 relative error = 9.13780214241607e-12 % Correct digits = 13 h = 1e-05 y1[1] (analytic) = 0.900067083435977 y1[1] (numeric) = 0.900067083435977 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10011 y2[1] (analytic) = 1.994993177582442 y2[1] (numeric) = 1.994993177582199 absolute error = 2.429167977879843e-13 relative error = 1.217632223095389e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000571334992042 y1[1] (numeric) = 0.9000571334992041 absolute error = 1.110223024625157e-16 relative error = 1.233502833657768e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10012 y2[1] (analytic) = 1.994992178104027 y2[1] (numeric) = 1.994992178103712 absolute error = 3.153033389935445e-13 relative error = 1.580474061272752e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000471835724256 y1[1] (numeric) = 0.9000471835724256 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10013 y2[1] (analytic) = 1.994991178526113 y2[1] (numeric) = 1.994991178525712 absolute error = 4.007905118896815e-13 relative error = 2.008983880248448e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000372336556425 y1[1] (numeric) = 0.9000372336556424 absolute error = 1.110223024625157e-16 relative error = 1.233530106433277e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.10014 y2[1] (analytic) = 1.9949901788487 y2[1] (numeric) = 1.994990178848199 absolute error = 5.007105841059456e-13 relative error = 2.509839844900407e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000272837488555 y1[1] (numeric) = 0.9000272837488554 absolute error = 1.110223024625157e-16 relative error = 1.233543743252737e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001499999999999 y2[1] (analytic) = 1.994989179071788 y2[1] (numeric) = 1.994989179071172 absolute error = 6.157296894571118e-13 relative error = 3.086381098786679e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000173338520658 y1[1] (numeric) = 0.9000173338520657 absolute error = 1.110223024625157e-16 relative error = 1.233557380360012e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001599999999999 y2[1] (analytic) = 1.994988179195377 y2[1] (numeric) = 1.99498817919463 absolute error = 7.474021401776554e-13 relative error = 3.746398840714431e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.9000073839652744 y1[1] (numeric) = 0.9000073839652744 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001699999999999 y2[1] (analytic) = 1.994987179219467 y2[1] (numeric) = 1.994987179218571 absolute error = 8.963940700823514e-13 relative error = 4.493232234369861e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.8999974340884822 y1[1] (numeric) = 0.8999974340884822 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001799999999999 y2[1] (analytic) = 1.994986179144059 y2[1] (numeric) = 1.994986179142995 absolute error = 1.06403774680075e-12 relative error = 5.3335594899072e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.8999874842216904 y1[1] (numeric) = 0.8999874842216903 absolute error = 1.110223024625157e-16 relative error = 1.2335982934088e-14 % Correct digits = 15 h = 1e-05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.1001899999999999 y2[1] (analytic) = 1.994985178969152 y2[1] (numeric) = 1.9949851789679 absolute error = 1.251665437962401e-12 relative error = 6.274058830898993e-11 % Correct digits = 12 h = 1e-05 y1[1] (analytic) = 0.8999775343648997 y1[1] (numeric) = 0.8999775343648997 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-05 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2 + 1.0; Iterations = 19 Total Elapsed Time = 1 Minutes 3 Seconds Elapsed Time(since restart) = 1 Minutes 2 Seconds Expected Time Remaining = 17 Days 20 Hours 43 Minutes 57 Seconds Optimized Time Remaining = 17 Days 13 Hours 55 Minutes 38 Seconds Time to Timeout Unknown Percent Done = 0.004082 %