##############ECHO OF PROBLEM################# ##############temp/sqrt_sqrtpostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=c(0.001) # 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(-2.0) # 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) #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(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 1.1372713678556832 y[1] (numeric) 1.1372713678556832 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y[1] (closed_form) 1.144044864944275 y[1] (numeric) 1.1440448649442754 absolute error 4.440892098500626e-16 relative error 3.881746454687279e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y[1] (closed_form) 1.1508263922859747 y[1] (numeric) 1.150826392285975 absolute error 2.220446049250313e-16 relative error 1.9294361548657836e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y[1] (closed_form) 1.1576159214548989 y[1] (numeric) 1.1576159214548996 absolute error 6.661338147750939e-16 relative error 5.754359476482431e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y[1] (closed_form) 1.164413424258851 y[1] (numeric) 1.164413424258852 absolute error 8.881784197001252e-16 relative error 7.627689626349427e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y[1] (closed_form) 1.171218872736315 y[1] (numeric) 1.171218872736316 absolute error 8.881784197001252e-16 relative error 7.583368406838226e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y[1] (closed_form) 1.1780322391535036 y[1] (numeric) 1.178032239153504 absolute error 4.440892098500626e-16 relative error 3.769754299501777e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y[1] (closed_form) 1.1848534960014563 y[1] (numeric) 1.1848534960014567 absolute error 4.440892098500626e-16 relative error 3.7480516481466906e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y[1] (closed_form) 1.191682615993191 y[1] (numeric) 1.1916826159931915 absolute error 4.440892098500626e-16 relative error 3.7265728633621354e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y[1] (closed_form) 1.1985195720608994 y[1] (numeric) 1.1985195720609 absolute error 6.661338147750939e-16 relative error 5.5579719372429755e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y[1] (closed_form) 1.2053643373531946 y[1] (numeric) 1.2053643373531953 absolute error 6.661338147750939e-16 relative error 5.5264105144991033e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y[1] (closed_form) 1.2122168852324038 y[1] (numeric) 1.2122168852324045 absolute error 6.661338147750939e-16 relative error 5.495170236367266e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y[1] (closed_form) 1.2190771892719083 y[1] (numeric) 1.2190771892719086 absolute error 2.220446049250313e-16 relative error 1.8214154680200934e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y[1] (closed_form) 1.225945223253526 y[1] (numeric) 1.2259452232535262 absolute error 2.220446049250313e-16 relative error 1.8112114694304935e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y[1] (closed_form) 1.232820961164941 y[1] (numeric) 1.232820961164941 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (closed_form) 1.2397043771971739 y[1] (numeric) 1.239704377197174 absolute error 2.220446049250313e-16 relative error 1.7911093080678485e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (closed_form) 1.2465954457420958 y[1] (numeric) 1.2465954457420958 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (closed_form) 1.2534941413899818 y[1] (numeric) 1.253494141389982 absolute error 2.220446049250313e-16 relative error 1.7714052071979308e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (closed_form) 1.260400438927108 y[1] (numeric) 1.2604004389271082 absolute error 2.220446049250313e-16 relative error 1.7616988860622945e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (closed_form) 1.267314313333384 y[1] (numeric) 1.2673143133333846 absolute error 6.661338147750939e-16 relative error 5.256263641676858e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (closed_form) 1.274235739780028 y[1] (numeric) 1.2742357397800286 absolute error 6.661338147750939e-16 relative error 5.2277125337112973e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (closed_form) 1.2811646936272763 y[1] (numeric) 1.2811646936272774 absolute error 1.1102230246251565e-15 relative error 8.665732283660237e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (closed_form) 1.2881011504221347 y[1] (numeric) 1.2881011504221358 absolute error 1.1102230246251565e-15 relative error 8.619067099360294e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (closed_form) 1.29504508589616 y[1] (numeric) 1.295045085896161 absolute error 1.1102230246251565e-15 relative error 8.572852302334261e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (closed_form) 1.3019964759632834 y[1] (numeric) 1.3019964759632843 absolute error 8.881784197001252e-16 relative error 6.821665312442612e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (closed_form) 1.3089552967176639 y[1] (numeric) 1.3089552967176648 absolute error 8.881784197001252e-16 relative error 6.785399179997371e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (closed_form) 1.3159215244315805 y[1] (numeric) 1.3159215244315814 absolute error 8.881784197001252e-16 relative error 6.749478621711722e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (closed_form) 1.3228951355533531 y[1] (numeric) 1.322895135553354 absolute error 8.881784197001252e-16 relative error 6.713898901205117e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (closed_form) 1.3298761067053002 y[1] (numeric) 1.3298761067053013 absolute error 1.1102230246251565e-15 relative error 8.348319208288335e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (closed_form) 1.3368644146817266 y[1] (numeric) 1.3368644146817275 absolute error 8.881784197001252e-16 relative error 6.643743448819212e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (closed_form) 1.3438600364469442 y[1] (numeric) 1.3438600364469453 absolute error 1.1102230246251565e-15 relative error 8.261448324339604e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (closed_form) 1.350862949133322 y[1] (numeric) 1.3508629491333233 absolute error 1.3322676295501878e-15 relative error 9.8623448840975e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (closed_form) 1.3578731300393687 y[1] (numeric) 1.3578731300393696 absolute error 8.881784197001252e-16 relative error 6.540952906803409e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (closed_form) 1.3648905566278418 y[1] (numeric) 1.3648905566278424 absolute error 6.661338147750939e-16 relative error 4.8804925167104476e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (closed_form) 1.37191520652389 y[1] (numeric) 1.3719152065238909 absolute error 8.881784197001252e-16 relative error 6.474003753851232e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (closed_form) 1.3789470575132206 y[1] (numeric) 1.3789470575132212 absolute error 6.661338147750939e-16 relative error 4.830742494033042e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (closed_form) 1.385986087540297 y[1] (numeric) 1.3859860875402972 absolute error 2.220446049250313e-16 relative error 1.6020695079204786e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (closed_form) 1.3930322747065624 y[1] (numeric) 1.3930322747065624 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (closed_form) 1.4000855972686923 y[1] (numeric) 1.400085597268692 absolute error 2.220446049250313e-16 relative error 1.5859359267619008e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (closed_form) 1.4071460336368704 y[1] (numeric) 1.4071460336368706 absolute error 2.220446049250313e-16 relative error 1.57797840179488e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 400 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.25000000000009%