ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 6s3k4pT2.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 6s3k4pT2.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 2.02e-05 | - | 3.75e-05 | - | 18 | 4.0000 | 0.2222 | 8.24e-06 | 3.56 | 1.39e-05 | 3.96 | 22 | 4.0000 | 0.1818 | 3.94e-06 | 3.68 | 6.24e-06 | 3.97 | 26 | 4.0000 | 0.1538 | 2.11e-06 | 3.74 | 3.21e-06 | 3.98 | 30 | 4.0000 | 0.1333 | 1.23e-06 | 3.78 | 1.81e-06 | 3.99 | 34 | 4.0000 | 0.1176 | 7.61e-07 | 3.82 | 1.10e-06 | 3.99 | 38 | 4.0000 | 0.1053 | 4.97e-07 | 3.84 | 7.06e-07 | 3.99 | 42 | 4.0000 | 0.0952 | 3.38e-07 | 3.86 | 4.74e-07 | 3.99 | errors = 1.0e-04 * 0.201678352638734 0.374747651792351 0.082373997477569 0.138566835169440 0.039400041814130 0.062416834737400 0.021090571907800 0.032091947299584 0.012271634584060 0.018139629138769 0.007612427156967 0.011009223192526 0.004967338111395 0.007062134181335 0.003376905589048 0.004735517727394 ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 7s4k5pT2.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 7s4k5pT2.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 1.29e-06 | - | 6.12e-07 | - | 18 | 4.0000 | 0.2222 | 3.80e-07 | 4.85 | 1.94e-07 | 4.58 | 22 | 4.0000 | 0.1818 | 1.42e-07 | 4.90 | 7.66e-08 | 4.62 | 26 | 4.0000 | 0.1538 | 6.25e-08 | 4.93 | 3.51e-08 | 4.67 | 30 | 4.0000 | 0.1333 | 3.08e-08 | 4.95 | 1.79e-08 | 4.71 | 34 | 4.0000 | 0.1176 | 1.65e-08 | 4.96 | 9.88e-09 | 4.75 | 38 | 4.0000 | 0.1053 | 9.52e-09 | 4.97 | 5.81e-09 | 4.78 | 42 | 4.0000 | 0.0952 | 5.79e-09 | 4.97 | 3.59e-09 | 4.80 | errors = 1.0e-05 * 0.128719427239243 0.061206649099033 0.038040413741225 0.019356162345163 0.014234680278946 0.007660592488135 0.006248572093082 0.003512408730533 0.003078232801990 0.001789851583611 0.001654572379106 0.000988087422993 0.000952095996487 0.000580912995485 0.000578703263088 0.000359345819767 ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 8s3k6pT2.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 8s3k6pT2.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 6.24e-08 | - | 1.35e-07 | - | 18 | 4.0000 | 0.2222 | 1.54e-08 | 5.56 | 2.91e-08 | 6.12 | 22 | 4.0000 | 0.1818 | 4.93e-09 | 5.68 | 8.59e-09 | 6.08 | 26 | 4.0000 | 0.1538 | 1.89e-09 | 5.74 | 3.12e-09 | 6.05 | 30 | 4.0000 | 0.1333 | 8.26e-10 | 5.78 | 1.32e-09 | 6.04 | 34 | 4.0000 | 0.1176 | 3.99e-10 | 5.81 | 6.19e-10 | 6.03 | 38 | 4.0000 | 0.1053 | 2.09e-10 | 5.83 | 3.17e-10 | 6.02 | 42 | 4.0000 | 0.0952 | 1.16e-10 | 5.85 | 1.73e-10 | 6.02 | errors = 1.0e-06 * 0.062413097967617 0.135273411416836 0.015428060995415 0.029068395801524 0.004934746111740 0.008586733213356 0.001890656298187 0.003123915848224 0.000826484936045 0.001316580677813 0.000399373367710 0.000619081175213 0.000208771944177 0.000316847659221 0.000116263443317 0.000173494385525 ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 8s3k7pT2.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 8s3k7pT2.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 1.25e-08 | - | 8.04e-09 | - | 18 | 4.0000 | 0.2222 | 2.14e-09 | 7.04 | 1.61e-09 | 6.41 | 22 | 4.0000 | 0.1818 | 5.13e-10 | 7.11 | 4.32e-10 | 6.55 | 26 | 4.0000 | 0.1538 | 1.56e-10 | 7.14 | 1.42e-10 | 6.64 | 30 | 4.0000 | 0.1333 | 5.60e-11 | 7.15 | 5.45e-11 | 6.71 | 34 | 4.0000 | 0.1176 | 2.29e-11 | 7.15 | 2.34e-11 | 6.76 | 38 | 4.0000 | 0.1053 | 1.03e-11 | 7.15 | 1.10e-11 | 6.79 | 42 | 4.0000 | 0.0952 | 5.05e-12 | 7.16 | 5.56e-12 | 6.82 | errors = 1.0e-07 * 0.125361004355007 0.080436894922542 0.021374555458920 0.016064594099419 0.005132456681878 0.004319194446545 0.001557821094345 0.001424171336417 0.000560158031071 0.000545358203041 0.000228894680987 0.000234128827437 0.000103346775582 0.000109973696816 0.000050494608494 0.000055579429947 ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 9s4k8p.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 9s4k8p.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 3.34e-10 | - | 1.12e-09 | - | 18 | 4.0000 | 0.2222 | 4.84e-11 | 7.68 | 7.58e-11 | 10.70 | 22 | 4.0000 | 0.1818 | 9.00e-12 | 8.39 | 6.78e-12 | 12.03 | 26 | 4.0000 | 0.1538 | 2.14e-12 | 8.58 | 4.19e-13 | 16.67 | 30 | 4.0000 | 0.1333 | 6.29e-13 | 8.57 | 1.52e-13 | 7.06 | 34 | 4.0000 | 0.1176 | 2.20e-13 | 8.39 | 1.30e-13 | 1.24 | 38 | 4.0000 | 0.1053 | 8.88e-14 | 8.16 | 7.92e-14 | 4.49 | 42 | 4.0000 | 0.0952 | 4.55e-14 | 6.68 | 4.36e-14 | 5.95 | errors = 1.0e-08 * 0.033364960794202 0.111582049155956 0.004841121947763 0.007582323657829 0.000899569307933 0.000677902178836 0.000214456230552 0.000041866510259 0.000062921889921 0.000015237811013 0.000022004620348 0.000013045120539 0.000008881784197 0.000007915890166 0.000004551914401 0.000004363176487 ODE Convergence Test Problem: < SSP_Tools.TestProblems.Vanderpol: y(0)=[ 0.50 0.00 ] epsilon=0.1 t=0 > Time Stepping Method: < SSP_Tools.Integrators.MSRK: MSRK 9s4k9p.mat priming=use-exact > Testing 14 Testing 18 Testing 22 Testing 26 Testing 30 Testing 34 Testing 38 Testing 42 Convergence Test Results Problem: Vanderpol y'=2y y(0)=[ 0.50 0.00 ] T=4.000000 Method: MSRK 9s4k9p.mat ---------------------------------------------------- N | T | dt | y1 Error | order | y2 Error | order | 14 | 4.0000 | 0.2857 | 6.12e-11 | - | 5.50e-11 | - | 18 | 4.0000 | 0.2222 | 6.40e-12 | 8.99 | 6.81e-12 | 8.31 | 22 | 4.0000 | 0.1818 | 9.88e-13 | 9.31 | 1.33e-12 | 8.15 | 26 | 4.0000 | 0.1538 | 2.06e-13 | 9.38 | 3.39e-13 | 8.16 | 30 | 4.0000 | 0.1333 | 5.80e-14 | 8.86 | 1.07e-13 | 8.07 | 34 | 4.0000 | 0.1176 | 2.37e-14 | 7.15 | 4.11e-14 | 7.63 | 38 | 4.0000 | 0.1053 | 1.24e-14 | 5.80 | 2.13e-14 | 5.91 | 42 | 4.0000 | 0.0952 | 1.27e-14 | -0.22 | 1.05e-14 | 7.03 | errors = 1.0e-10 * 0.612431771962463 0.550343659533326 0.064003247146616 0.068149930143591 0.009875433804041 0.013267165144271 0.002061684156729 0.003393951786279 0.000580091530367 0.001069144772714 0.000237032615757 0.000411337630624 0.000124344978758 0.000213162820728 0.000127120536320 0.000105471187339