##############ECHO OF PROBLEM################# ##############temp/lin_arccos_0d2_0d5postode.ode################# diff ( y , x , 1 ) = arccos ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.2); x_end=c(0.5); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_display_interval=0.0001; glob_type_given_pole=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=true; 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(x) *arccos(c(x)) - sqrt(glob__1 - c(x) * c(x))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = -0.705908215912358 y[1] (numeric) = -0.705908215912358 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.21 y[1] (closed_form) = -0.6922648988269866 y[1] (numeric) = -0.69226489846308 absolute error = 3.639065715432821e-10 relative error = 5.256753190287508e-08 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 10 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.22 y[1] (closed_form) = -0.6787238634749932 y[1] (numeric) = -0.6787238627268863 absolute error = 7.481069097536874e-10 relative error = 1.102225735696783e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.23 y[1] (closed_form) = -0.6652853407037465 y[1] (numeric) = -0.6652853395507531 absolute error = 1.152993367448119e-09 relative error = 1.733080975793738e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.24 y[1] (closed_form) = -0.6519495737795037 y[1] (numeric) = -0.65194957220052 absolute error = 1.578983721550742e-09 relative error = 2.421941489120094e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (closed_form) = -0.6387168186386497 y[1] (numeric) = -0.6387168166121265 absolute error = 2.026523171494432e-09 relative error = 3.172803834747501e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (closed_form) = -0.6255873441553936 y[1] (numeric) = -0.6255873416593078 absolute error = 2.496085782510704e-09 relative error = 3.989987658527001e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (closed_form) = -0.6125614324267578 y[1] (numeric) = -0.6125614294385818 absolute error = 2.988175928919645e-09 relative error = 4.878165308386328e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (closed_form) = -0.5996393790757606 y[1] (numeric) = -0.5996393755724305 absolute error = 3.503330070486754e-09 relative error = 5.842394933912655e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (closed_form) = -0.5868214935737708 y[1] (numeric) = -0.5868214895316526 absolute error = 4.042118195712874e-09 relative error = 6.88815634733517e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000001 y[1] (closed_form) = -0.5741080995830958 y[1] (numeric) = -0.57410809497795 absolute error = 4.605145820235634e-09 relative error = 8.021391482857994e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000001 y[1] (closed_form) = -0.5614995353209528 y[1] (numeric) = -0.561499530127897 absolute error = 5.193055763186294e-09 relative error = 9.248548638990319e-07 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 9 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000001 y[1] (closed_form) = -0.5489961539460755 y[1] (numeric) = -0.5489961481395439 absolute error = 5.806531588881114e-09 relative error = 1.057663436646125e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000001 y[1] (closed_form) = -0.5365983239693088 y[1] (numeric) = -0.5365983175230101 absolute error = 6.446298717044385e-09 relative error = 1.201326658898228e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000001 y[1] (closed_form) = -0.5243064296896697 y[1] (numeric) = -0.5243064225765425 absolute error = 7.113127198365987e-09 relative error = 1.356673654102651e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000001 y[1] (closed_form) = -0.5121208716574744 y[1] (numeric) = -0.5121208638496384 absolute error = 7.807836044371186e-09 relative error = 1.524608051825968e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (closed_form) = -0.5000420671662755 y[1] (numeric) = -0.5000420586349815 absolute error = 8.53129400457675e-09 relative error = 1.706115258046859e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (closed_form) = -0.4880704507755111 y[1] (numeric) = -0.4880704414910856 absolute error = 9.284425506184135e-09 relative error = 1.902271586290833e-06 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (closed_form) = -0.4762064748659323 y[1] (numeric) = -0.4762064647977194 absolute error = 1.006821287452553e-08 relative error = 2.114253670607914e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (closed_form) = -0.4644506102300692 y[1] (numeric) = -0.4644505993463688 absolute error = 1.088370044088904e-08 relative error = 2.343349368299402e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (closed_form) = -0.4528033467002043 y[1] (numeric) = -0.4528033349682044 absolute error = 1.173199992710039e-08 relative error = 2.590970233015528e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000002 y[1] (closed_form) = -0.4412651938165476 y[1] (numeric) = -0.4412651812022529 absolute error = 1.261429460885921e-08 relative error = 2.8586652166596e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000002 y[1] (closed_form) = -0.4298366815385696 y[1] (numeric) = -0.4298366680067248 absolute error = 1.353184486685421e-08 relative error = 3.148136361563639e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000002 y[1] (closed_form) = -0.4185183610027295 y[1] (numeric) = -0.4185183465167359 absolute error = 1.448599362685599e-08 relative error = 3.461256417077842e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000002 y[1] (closed_form) = -0.4073108053301534 y[1] (numeric) = -0.4073107898519789 absolute error = 1.547817451985622e-08 relative error = 3.800089346343292e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000002 y[1] (closed_form) = -0.3962146104881672 y[1] (numeric) = -0.3962145939782503 absolute error = 1.65099169335825e-08 relative error = 4.166912702497518e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000002 y[1] (closed_form) = -0.3852303962099899 y[1] (numeric) = -0.3852303786271348 absolute error = 1.758285511632707e-08 relative error = 4.564243966548948e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (closed_form) = -0.3743588069773272 y[1] (numeric) = -0.3743587882785906 absolute error = 1.869873650361953e-08 relative error = 4.994870203428127e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (closed_form) = -0.3636005130711041 y[1] (numeric) = -0.3636004932116726 absolute error = 1.985943143267832e-08 relative error = 5.461882125780911e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (closed_form) = -0.3529562116961332 y[1] (numeric) = -0.3529561906291895 absolute error = 2.106694374504059e-08 relative error = 5.968713128408553e-06 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 8 h = 0.001 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos ( x ) ; Iterations = 300 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.3 %