##############ECHO OF PROBLEM################# ##############temp/expt_sin_sin_new_sm_hpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ), sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) )) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin( 2.0 * x + 3.0 ) ) ); ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=1.8; x_end=1.81; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_max_h=0.000001; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.001; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(expt(sin(2.0*x+3.0),sin(x+1.0))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.01000000000000001 estimated_steps = 10000.00000000001 step_error = 9.999999999999991e-15 est_needed_step_err = 9.999999999999991e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.146572728549469e-137 max_value3 = 1.146572728549469e-137 value3 = 1.146572728549469e-137 best_h = 1e-06 START of Soultion TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.6766027626496453 y[1] (numeric) = 0.6766027626496453 absolute error = 0 relative error = 0 % Correct digits = 16 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.801000999999918 y[1] (analytic) = 0.6787259139185762 y[1] (numeric) = 0.6787259102669944 absolute error = 3.651581814700933e-09 relative error = 5.380053626682357e-07 % Correct digits = 8 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.802000999999835 y[1] (analytic) = 0.6808368151795497 y[1] (numeric) = 0.6808368079358343 absolute error = 7.243715405280682e-09 relative error = 1.063942966035169e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.803000999999753 y[1] (analytic) = 0.6829376415361824 y[1] (numeric) = 0.6829376307552721 absolute error = 1.078091027562067e-08 relative error = 1.578608297438455e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.804000999999671 y[1] (analytic) = 0.6850284413339742 y[1] (numeric) = 0.685028427069999 absolute error = 1.426397522319434e-08 relative error = 2.082245694122964e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.805000999999589 y[1] (analytic) = 0.6871092622848669 y[1] (numeric) = 0.6871092445911511 absolute error = 1.769371582582835e-08 relative error = 2.575094937156117e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.806000999999506 y[1] (analytic) = 0.6891801514826514 y[1] (numeric) = 0.6891801304117373 absolute error = 2.107091412462125e-08 relative error = 3.057388417134597e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.807000999999424 y[1] (analytic) = 0.6912411554179351 y[1] (numeric) = 0.6912411310215897 absolute error = 2.439634538831115e-08 relative error = 3.529353713547443e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.808000999999342 y[1] (analytic) = 0.6932923199926818 y[1] (numeric) = 0.69329229232192 absolute error = 2.767076179299721e-08 relative error = 3.991211354149906e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 TOP MAIN SOLVE Loop x[1] = 1.80900099999926 y[1] (analytic) = 0.6953336905343417 y[1] (numeric) = 0.6953336596394286 absolute error = 3.089491307228798e-08 relative error = 4.443177929225064e-06 % Correct digits = 7 h = 1e-06 NO POLE for equation 1 Finished! diff ( y , x , 1 ) = expt ( sin ( 2.0 * x + 3.0 ), sin ( x + 1.0 ) ) * ( ( cos ( x + 1.0 ) * ln ( sin ( 2.0 * x + 3.0 ) )) + ( ( 2.0 * sin ( x + 1.0 ) * cos ( 2.0 * x + 3.0 ) ) / sin( 2.0 * x + 3.0 ) ) ); Iterations = 10001 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 59 Seconds Percent Done = 100 %