Method 1/5,[1:5,5]/5, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
| 0.2 | 0 | 0 | 0 | -0 | 0 |
| 0.119424 | 0.2 | 0 | 0 | -0 | 0 |
| -5.68121 | 3.32904 | 0.2 | 0 | -0 | 0 |
| 2.80411 | -0.901561 | -0.0973527 | 0.2 | 0 | 0 |
| -1.98421 | 1.87326 | -0.0936676 | 0.0944223 | 0.2 | 0 |
| 1.81029 | -0.806963 | 0.135685 | 0.460284 | -0.216237 | 0.2 |
|
| 1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
| 1 | 0.0805759 | -0.0477696 | -0.0463309 | -0.0294216 | -0.0163154 |
| 1 | 2.75216 | -0.270753 | -0.916196 | -0.713637 | -0.432508 |
| 1 | -1.2052 | 0.0364263 | 0.329397 | 0.225181 | 0.0741314 |
| 1 | 0.910196 | -0.1436 | -0.341191 | -0.328509 | -0.356584 |
| 1 | -0.583057 | 0.0546528 | 0.188533 | 0.153707 | 0.139407 |
|
| 1.81029 | -0.806963 | 0.135685 | 0.460284 | -0.216237 | 0.2 |
| -0 | 0 | 0 | 0 | 0 | 1 |
| 1.17157 | 3.504 | -3.4959 | -4.07136 | 4.25614 | -0.0984219 |
| 7.23678 | 6.22988 | -6.92071 | -7.47975 | 8.0679 | -2.09076 |
| 6.58622 | 6.7687 | -6.64797 | -5.75099 | 7.7902 | -3.50168 |
| 1.61187 | 2.67233 | -2.43143 | -1.5568 | 2.96773 | -1.76763 |
|
| 1 | -0.583057 | 0.0546528 | 0.188533 | 0.153707 | 0.139407 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -1.26603 | 0.121987 | 0.296909 | -0.206802 | -0.64301 |
| 0 | -5.04335 | 0.439539 | 1.04529 | -0.436992 | -0.937903 |
| 0 | -5.24448 | 0.552658 | 1.31683 | -0.575752 | -1.27577 |
| 0 | -1.49607 | 0.225792 | 0.538576 | -0.246987 | -0.591524 |
|
Maximum coefficient scaled is 8.067904 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.0049,-0.0109,-0.0201,0.1962],[ -0.752123 0.0572144 0.0422964 1; 1 0 0 0; 0.656447 1 0 0; -0.386466 -0.775752 1 0; ])
[alpha,beta,gamma,stageerror]
| -0.000133778 | 0.00235272 | -0.00254418 | 0.000128549 |
| 0 | 0 | -0 | 0.000187472 |
| -0.0049 | 0.00343381 | -0.00247243 | 0.00188456 |
| -0.0109 | 0.0315306 | -0.034292 | -0.000804536 |
| -0.0201 | 0.145261 | -0.152217 | 3.42814e-05 |
| 0.1962 | 0.248587 | -0.307181 | -0.000133778 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[15625.000000 -31250.000000 31250.000000 -15625.000000 -399831.548291 402956.548291 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | 0 | 0 | 0 | 0 | 0 |
| 10.8414 | -0.518662 | -0.391403 | -0.078977 | -0.0197981 | -0.00451079 |
| -0.51109 | -0.106502 | -0.0455414 | -0.246596 | -0.0670963 | 0.00718946 |
| -71.0093 | 4.00392 | 3.25577 | -0.829027 | -0.292406 | 0.0958136 |
| -715.011 | 39.1997 | 30.4065 | 1.23733 | -0.227903 | 0.593094 |
| -2729.27 | 130.745 | 100.076 | 12.6007 | 1.85332 | 1.62113 |
Method 1/5,[1:5,5]/5, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
| 0.2 | -0 | 0 | 0 | -0 | -0 |
| -0.00679235 | 0.2 | 0 | 0 | -0 | -0 |
| -1.62098 | 0.670688 | 0.2 | 0 | -0 | -0 |
| -1.28601 | -0.115973 | 0.391005 | 0.2 | -0 | -0 |
| -2.40282 | -0.253638 | 0.203504 | 0.377653 | 0.2 | -0 |
| -3.94664 | -4.00387 | 3.60139 | 2.29958 | -1.70817 | 0.2 |
|
| 1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
| 1 | 0.206792 | 0.00271694 | -0.0311849 | -0.0253826 | -0.0153057 |
| 1 | 1.35029 | 0.231841 | -0.127413 | -0.163025 | -0.12472 |
| 1 | 1.61098 | 0.457976 | -0.0842971 | -0.266987 | -0.310159 |
| 1 | 2.8753 | 0.915588 | -0.134795 | -0.60744 | -0.853617 |
| 1 | 4.55771 | 0.797102 | -0.384722 | 0.362832 | 2.04169 |
|
| -3.94664 | -4.00387 | 3.60139 | 2.29958 | -1.70817 | 0.2 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 3.95242 | 5.34019 | -5.34415 | -5.38626 | 4.33701 | 0.754927 |
| 4.991 | -3.9846 | -5.39581 | 1.19821 | 2.32063 | -0.347257 |
| -3.28741 | 3.1882 | -1.47334 | -2.62477 | 2.03561 | -0.142579 |
| 2.18021 | -4.45498 | 0.315927 | 1.70122 | -0.312697 | -0.258529 |
|
| 1 | 4.55771 | 0.797102 | -0.384722 | 0.362832 | 2.04169 |
| 0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -3.65413 | -0.00599295 | 0.799914 | -0.212901 | -1.68077 |
| 0 | 1.21783 | 1.80237 | -0.0795255 | -0.825109 | 1.64578 |
| 0 | 2.3043 | 0.945997 | -0.184157 | -0.634594 | 1.48333 |
| 0 | 0.828852 | 0.73329 | -0.0170969 | -0.401442 | 0.720112 |
|
Maximum coefficient scaled is 5.395814 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.0225,-0.0621,0.0451,-0.0897],[ -0.00318701 1 0 0; 0.122793 -0.563594 -0.23714 1; 0.267692 -0.63941 1 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000133778 | 0.0381237 | -0.0383151 | 0.000607092 |
| 0 | -0 | 0 | 0.000244581 |
| -0.0225 | 0.0248104 | -0.0268287 | -0.00162033 |
| -0.0621 | 0.276962 | -0.305033 | -0.00497172 |
| 0.0451 | 0.495814 | -0.553868 | -0.0108215 |
| -0.0897 | 2.18954 | -2.15249 | -0.000133778 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[15625.000000 -31250.000000 31250.000000 -15625.000000 2664.039762 460.960238 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | -0 | -0 | -0 | -0 | -0 |
| -479.643 | -28.0848 | 11.1243 | 2.42394 | 0.153822 | -0.0366096 |
| -1296.34 | -72.0904 | 29.8877 | 6.53277 | 0.584154 | -0.00823874 |
| 1002.07 | 67.6344 | -22.5002 | -5.52881 | -0.0678135 | 0.367775 |
| -1783.58 | -67.9434 | 42.944 | 7.72696 | 1.44503 | 0.919229 |
| 20992.7 | 1247.95 | -482.564 | -108.519 | -8.08157 | 2.28091 |
Method 1/5,[1:5,5]/5,big=4.30, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
| 0.2 | -0 | 0 | 0 | -0 | -0 |
| 0.00736578 | 0.2 | 0 | 0 | -0 | -0 |
| 0.657222 | -0.304818 | 0.2 | 0 | -0 | -0 |
| -1.05142 | -0.600342 | 0.687448 | 0.2 | 0 | -0 |
| -0.592772 | -0.752277 | 0.0224103 | 0.455995 | 0.2 | -0 |
| -3.84413 | -0.541829 | 2.02772 | 1.79011 | -1.52111 | 0.2 |
|
| 1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
| 1 | 0.192634 | -0.00294631 | -0.0328839 | -0.0258357 | -0.0154189 |
| 1 | 0.0475958 | 0.100966 | 0.067446 | 0.0138023 | -0.0180811 |
| 1 | 1.56432 | 0.395905 | -0.200109 | -0.406622 | -0.442131 |
| 1 | 1.66664 | 0.682446 | -0.0674877 | -0.541689 | -0.847366 |
| 1 | 2.88924 | 0.3159 | 0.0577575 | 1.12807 | 2.72555 |
|
| -3.84413 | -0.541829 | 2.02772 | 1.79011 | -1.52111 | 0.2 |
| 0 | 0 | -0 | 0 | 0 | 1 |
| 2.07313 | -2.92661 | -4.03584 | 0.902046 | 2.01787 | 0.340336 |
| 4.36325 | -4.29908 | -2.44352 | -0.82197 | 2.5104 | -0.0893124 |
| -3.12703 | -2.4696 | 0.842445 | -0.306479 | 1.02871 | -0.271774 |
| -1.91361 | -0.535689 | 0.183671 | 0.572782 | -0.0382281 | -0.144698 |
|
| 1 | 2.88924 | 0.3159 | 0.0577575 | 1.12807 | 2.72555 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1.62906 | 1.19535 | -0.291858 | -1.1104 | -0.6652 |
| 0 | 0.78023 | 1.09916 | -0.506123 | -0.928831 | 1.67671 |
| 0 | 4.30372 | 1.19205 | -1.03155 | -1.39566 | 1.63822 |
| 0 | 1.87577 | 0.422993 | -0.262563 | -0.401672 | 0.706432 |
|
Maximum coefficient scaled is 4.363250 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.049751,-0.045373,-0.044267,0.175643],[ 0.0564427 0.0139217 1 0; -0.189671 0.178258 0.34646 1; 1 0 0 0; -0.594401 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000133778 | 0.0603722 | -0.0605636 | 0.00112255 |
| -0 | 0 | -0 | 0.000335651 |
| -0.049751 | 0.0765788 | -0.0678404 | -0.00311407 |
| -0.045373 | 0.242137 | -0.283918 | -0.00880571 |
| -0.044267 | 0.302063 | -0.33966 | -0.0181787 |
| 0.175643 | 1.3426 | -1.41772 | -0.000133778 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[15625.000000 -31250.000000 31250.000000 -15625.000000 2599.463568 525.536432 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | 0 | 0 | 0 | 0 | 0 |
| 1124.65 | 38.2472 | -43.2393 | -11.2552 | -1.7972 | -0.241629 |
| 1027.39 | 37.0888 | -39.8517 | -10.4126 | -1.5451 | -0.152533 |
| 1101.07 | 47.2723 | -42.5127 | -11.3279 | -1.26159 | 0.143052 |
| -3733.9 | -105.43 | 147.059 | 37.401 | 7.0122 | 1.85125 |
| -22540 | -744.746 | 867.158 | 224.372 | 35.9011 | 5.9202 |
Method 1/5,[1:5,5]/5,big=4.16 (John), c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
| 0.2 | 0 | 0 | 0 | -0 | 0 |
| -0.00681348 | 0.2 | -0 | 0 | -0 | 0 |
| -1.36481 | 0.559054 | 0.2 | -0 | -0 | -0 |
| -0.870026 | -0.48069 | 0.498894 | 0.2 | -0 | 0 |
| -1.55472 | -0.859501 | 0.265377 | 0.427024 | 0.2 | -0 |
| -3.77912 | -3.22578 | 3.47016 | 1.69329 | -1.43177 | 0.2 |
|
| 1 | -0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
| 1 | 0.206813 | 0.00272539 | -0.0311824 | -0.025382 | -0.0153055 |
| 1 | 1.20575 | 0.21868 | -0.104569 | -0.142644 | -0.11248 |
| 1 | 1.45182 | 0.453889 | -0.0756715 | -0.280147 | -0.336715 |
| 1 | 2.52182 | 0.907798 | -0.107366 | -0.634047 | -0.924055 |
| 1 | 4.07323 | 0.68236 | -0.301709 | 0.407735 | 1.88546 |
|
| -3.77912 | -3.22578 | 3.47016 | 1.69329 | -1.43177 | 0.2 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 4.16318 | 2.33226 | -4.16318 | -4.16318 | 3.63457 | 0.790274 |
| 0.989946 | -4.16318 | -4.16318 | 1.64253 | 1.84847 | -0.317764 |
| -2.88985 | 1.29238 | -0.70051 | -2.03934 | 1.68677 | -0.131116 |
| 1.11622 | -4.16318 | 0.599904 | 1.54818 | -0.304415 | -0.257291 |
|
| 1 | 4.07323 | 0.68236 | -0.301709 | 0.407735 | 1.88546 |
| 0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -2.59393 | 0.276134 | 0.595939 | -0.306481 | -1.23213 |
| 0 | 4.16318 | 2.24093 | -0.370004 | -0.855638 | 2.20528 |
| 0 | 2.78165 | 1.11427 | -0.268454 | -0.679197 | 1.70991 |
| 0 | 1.46058 | 0.810488 | -0.0709134 | -0.412121 | 0.773066 |
|
Maximum coefficient scaled is 4.163182 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.0221504,-0.0635424,0.0413678,-0.0980793],[ 0.000771702 -0.558108 -0.479786 1; 0.140418 0.786611 1 0; 0.296421 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000133778 | 0.0417241 | -0.0419156 | 0.000604782 |
| 0 | -0 | 0 | 0.00025745 |
| -0.0221504 | 0.0313358 | -0.0335083 | -0.00157729 |
| -0.0635424 | 0.315894 | -0.344276 | -0.00489518 |
| 0.0413678 | 0.570777 | -0.630262 | -0.0107929 |
| -0.0980793 | 2.29976 | -2.26801 | -0.000133778 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[15625.000000 -31250.000000 31250.000000 -15625.000000 2644.036909 480.963091 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | -0 | -0 | -0 | -0 | -0 |
| -524.634 | -29.352 | 10.8605 | 2.11759 | 0.0933447 | -0.0384981 |
| -1465.15 | -78.2708 | 30.2155 | 5.93405 | 0.43695 | -0.0163831 |
| 1036.87 | 68.7043 | -20.9858 | -4.68168 | 0.1293 | 0.39469 |
| -2124.78 | -82.5604 | 45.7913 | 7.42892 | 1.27731 | 0.898903 |
| 23450.9 | 1337.59 | -481.341 | -96.7536 | -5.14123 | 2.54079 |