Method 22.4735, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | 0 | 0 | -0 | -0 | -0 | 0 |
| 0.0231246 | 0.25 | 0 | -0 | -0 | -0 | 0 |
| -0.475908 | 0.227712 | 0.25 | -0 | -0 | 0 | 0 |
| -0.840762 | -0.058571 | 0.250498 | 0.25 | -0 | 0 | 0 |
| -3.59167 | 6.38412 | -5.61121 | 1.82965 | 0.25 | -0 | 0 |
| -0.56564 | -1.11331 | 0.115295 | -0.173865 | 0.415186 | 0.25 | 0 |
| 5.86195 | -10.2328 | 0.255108 | 5.74512 | -0.448288 | -1.10198 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | 0.0602087 | -0.0632638 | -0.0482233 | -0.0251196 | -0.0114061 | -0.00481894 |
| 1 | 0.498196 | 0.00682806 | -0.098745 | -0.087422 | -0.0590952 | -0.0365053 |
| 1 | 1.0655 | 0.179915 | -0.135323 | -0.199767 | -0.186648 | -0.154613 |
| 1 | 1.57244 | 0.390597 | -0.00198976 | -0.338603 | -0.634722 | -0.816327 |
| 1 | 2.07233 | 0.8553 | -0.0513829 | -0.637255 | -1.04453 | -1.35744 |
| 1 | 0.670852 | 0.403704 | -0.439179 | -0.0835317 | 1.19599 | 2.8538 |
|
| 5.86195 | -10.2328 | 0.255108 | 5.74512 | -0.448288 | -1.10198 | 0.25 |
| -0 | -0 | -0 | 0 | 0 | 0 | 1 |
| 5.33791 | -0.335807 | 2.51769 | -10.3565 | 2.41458 | 1.92538 | 0.998104 |
| 14.9564 | -13.7675 | 13.4115 | -16.2124 | 1.85597 | 3.18671 | 0.56794 |
| -1.92348 | 12.9193 | -11.3334 | -2.89127 | 0.157175 | 2.24588 | 0.0671324 |
| -4.65617 | 17.9724 | -22.4735 | 7.24936 | 0.434888 | 0.196953 | -0.213323 |
| 2.15248 | 1.81539 | -6.57149 | 3.15887 | 0.417618 | -0.27032 | -0.109463 |
|
| 1 | 0.670852 | 0.403704 | -0.439179 | -0.0835317 | 1.19599 | 2.8538 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -2.50131 | 0.864337 | 0.786744 | -0.31676 | -0.997565 | -0.648037 |
| 0 | -3.99863 | 1.7953 | 0.770141 | -1.04323 | -0.635195 | 3.62039 |
| 0 | 0.758625 | 2.32871 | 0.942439 | -1.40084 | -1.33685 | 4.83491 |
| 0 | 1.48939 | 1.68607 | 0.729613 | -0.872647 | -1.19512 | 3.09531 |
| 0 | -0.593084 | 0.495445 | 0.201598 | -0.214485 | -0.294719 | 0.961483 |
|
Maximum coefficient scaled is 22.473494 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [-0.00635614,-0.0145191,-0.0381262,-0.101644,0.0748033],[ -0.0107101 0.023209 -0.2245 0.871571 1; 0.0407521 -0.0142975 0.17394 1 0; 0.0224275 0.224447 1 0 0; -0.0593363 1 0 0 0; 1 0 0 0 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | 0.0130814 | -0.0128922 | 0.000222582 |
| -0 | 0 | -0 | 0.000366429 |
| -0.00635614 | 0.00644205 | -0.00596659 | 0.000398093 |
| -0.0145191 | 0.083428 | -0.0886981 | 0.000190892 |
| -0.0381262 | 0.286038 | -0.297705 | -0.000420101 |
| -0.101644 | 0.950273 | -0.980796 | -0.0011589 |
| 0.0748033 | 2.33621 | -2.44345 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000000 699840.000000 -933120.000000 699840.000000 -279936.000000 62383.232567 -15727.232567 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | 0 | 0 | 0 | 0 | 0 |
| 490.961 | 8.02392 | -3.6414 | -0.104227 | -0.0865328 | -0.0461995 | -0.0111822 |
| 1108.92 | 21.7403 | -8.14682 | -0.438593 | -0.191445 | -0.0712498 | -0.0109517 |
| 2993.15 | 70.89 | -19.6456 | -1.86769 | -0.686692 | -0.105158 | 0.032211 |
| 8109.89 | 215.656 | -47.8327 | -5.60786 | -2.31303 | -0.194125 | 0.241861 |
| -6263.85 | 94.1015 | 70.1326 | -5.51858 | -0.945604 | 1.484 | 1.19886 |
| -78029 | -1126.4 | 614.154 | 12.245 | 10.9983 | 6.98527 | 2.81962 |
Method 49.1568, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | 0 | -0 | 0 | -0 | 0 | 0 |
| 0.111161 | 0.25 | 0 | -0 | 0 | -0 | -0 |
| 0.410887 | 0.0479883 | 0.25 | -0 | 0 | -0 | -0 |
| 4.72666 | -2.98092 | 0.904577 | 0.25 | 0 | -0 | -0 |
| 19.4929 | -1.01349 | -9.76688 | 4.31363 | 0.25 | -0 | -0 |
| 44.1006 | 4.72202 | -30.5459 | 13.0345 | -0.239517 | 0.25 | -0 |
| 33.2279 | -10.885 | -6.74541 | 0.878611 | 2.40419 | -0.44856 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | -0.0278277 | -0.0926092 | -0.0555597 | -0.0267499 | -0.0117457 | -0.00488687 |
| 1 | -0.208875 | -0.168954 | -0.112737 | -0.0772184 | -0.0514225 | -0.0327519 |
| 1 | -2.23365 | -0.381737 | -0.115716 | -0.196966 | -0.232134 | -0.209392 |
| 1 | -12.4428 | -1.52881 | 0.344948 | -0.536293 | -1.42181 | -1.83494 |
| 1 | -30.3216 | -3.7824 | 1.03008 | -1.13711 | -3.46204 | -4.64457 |
| 1 | -17.6817 | -0.855232 | 1.33387 | -0.442359 | -2.02044 | -2.79209 |
|
| 33.2279 | -10.885 | -6.74541 | 0.878611 | 2.40419 | -0.44856 | 0.25 |
| 0 | -0 | -0 | 0 | 0 | 0 | 1 |
| 10.2585 | -45.7602 | 41.031 | 14.1662 | -37.3108 | 12.0993 | 3.05285 |
| 16.0199 | -16.9639 | -0.706527 | 27.6735 | -33.4202 | 10.3744 | 2.45468 |
| -43.0752 | 49.1568 | -26.1255 | 26.1191 | -30.1601 | 9.75209 | 1.83285 |
| -25.5917 | 26.5436 | -10.8358 | 8.9523 | -11.4982 | 3.81237 | 0.647319 |
| -4.00907 | 3.6605 | -0.984947 | 1.09154 | -1.78538 | 0.604905 | 0.096179 |
|
| 1 | -17.6817 | -0.855232 | 1.33387 | -0.442359 | -2.02044 | -2.79209 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 2.46309 | 0.048288 | 0.0112467 | 1.04307 | 0.176918 | -3.71129 |
| 0 | -5.43184 | -0.180004 | 0.0896944 | -0.183226 | 0.313831 | 2.28396 |
| 0 | 12.4999 | -0.0158741 | 0.0513298 | 0.097214 | -0.701357 | 1.29502 |
| 0 | 7.97007 | -0.0215368 | 0.0506741 | 0.126677 | -0.568659 | 1.28964 |
| 0 | 1.32627 | -0.000953712 | 0.0135354 | 0.0592318 | -0.18115 | 0.333462 |
|
Maximum coefficient scaled is 49.156845 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [-0.00760196,0.0349998,0.0538775,0.35479,0.871726],[ 0.19426 -0.241491 1 0 0; 1 0 0 0 0; -0.249644 0.446928 0.107173 -0.18307 1; 0.850736 1 0 0 0; -0.565594 0.40268 0.584975 1 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | -0.00843344 | 0.0086227 | 0.000105298 |
| 0 | -0 | -0 | -7.31739e-05 |
| -0.00760196 | 0.00764226 | -0.00101543 | -0.000384448 |
| 0.0349998 | -0.0519436 | 0.0138315 | -0.000639008 |
| 0.0538775 | -0.0309014 | 0.0189348 | -0.000179643 |
| 0.35479 | -0.254478 | -0.000924968 | 0.000999566 |
| 0.871726 | -0.411493 | 0.00637784 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000001 699840.000002 -933120.000002 699840.000001 -279936.000000 126895.654852 -80239.654852 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 3.83206e-09 | -1.60036e-10 | -0 | 0 | 0 | 0 | 0 |
| 561.711 | -22.6778 | -8.74205 | 0.400446 | 0.233934 | 0.0304358 | 0.00246967 |
| -2596.06 | 104.092 | 40.3557 | -1.48929 | -1.04777 | -0.168558 | -0.0222223 |
| -3646.11 | 160.877 | 62.1895 | -2.12483 | -1.77733 | -0.245605 | 0.00552012 |
| -25029.3 | 1059.36 | 409.188 | -13.9991 | -11.3489 | -1.68666 | -0.0172594 |
| -62892.3 | 2605.69 | 1004.52 | -34.1752 | -27.5742 | -4.3388 | 0.0571217 |
| -73242.3 | 2989.51 | 1150.47 | -41.2425 | -30.3849 | -5.35979 | 0.134657 |
Method 25.7853, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | 0 | -0 | 0 | 0 | -0 | 0 |
| 0.0457411 | 0.25 | -0 | 0 | 0 | -0 | 0 |
| -0.325051 | 0.101754 | 0.25 | 0 | 0 | -0 | 0 |
| 3.28228 | -5.60527 | 2.15808 | 0.25 | 0 | -0 | 0 |
| 12.0349 | -14.7208 | -6.4336 | 7.04925 | 0.25 | -0 | 0 |
| 21.8756 | -25.7853 | -13.0958 | 13.3747 | 0.0690274 | 0.25 | 0 |
| 12.0797 | -13.3826 | -11.2645 | 9.34903 | 0.680738 | -0.226613 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | 0.0375922 | -0.0708026 | -0.0501081 | -0.0255384 | -0.0114933 | -0.00483639 |
| 1 | 0.473297 | 0.0405145 | -0.0693303 | -0.0715552 | -0.051902 | -0.0335116 |
| 1 | 0.581585 | 0.595792 | -0.0606921 | -0.408175 | -0.456283 | -0.378509 |
| 1 | 2.65365 | 3.11465 | -0.611887 | -3.27632 | -4.2904 | -4.2772 |
| 1 | 4.31175 | 5.54618 | -1.13272 | -6.0484 | -8.02626 | -8.15882 |
| 1 | 3.51428 | 3.51301 | -1.0511 | -4.35848 | -5.69233 | -5.73543 |
|
| 12.0797 | -13.3826 | -11.2645 | 9.34903 | 0.680738 | -0.226613 | 0.25 |
| -0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 24.7241 | -20.8568 | 6.02382 | 2.17369 | -5.50599 | 1.26234 | 2.30306 |
| -9.14654 | 10.3474 | 1.74847 | 9.12014 | -25.1778 | 14.7683 | -2.59986 |
| -16.3469 | 4.08322 | 18.368 | 1.98861 | -24.8425 | 16.5577 | -4.88204 |
| -5.18773 | -4.13118 | 13.3837 | -1.43675 | -9.52864 | 6.71805 | -2.26097 |
| 2.31748 | -4.88413 | 4.6513 | -0.790018 | -1.5165 | 1.12379 | -0.41268 |
|
| 1 | 3.51428 | 3.51301 | -1.0511 | -4.35848 | -5.69233 | -5.73543 |
| 0 | -0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -10.1243 | -0.213089 | 1.25041 | 1.52765 | 2.61218 | 4.53297 |
| 0 | 0.93984 | -0.132025 | 0.789878 | 0.561205 | -0.289384 | -0.0827897 |
| 0 | 5.07388 | -0.239864 | 0.301841 | -0.0400229 | -1.3696 | -0.255688 |
| 0 | 2.4435 | -0.0177896 | 0.167332 | -0.0522433 | -0.797709 | 0.965352 |
| 0 | -0.489247 | -0.00906754 | 0.0258545 | -0.042686 | -0.279569 | 0.260942 |
|
Maximum coefficient scaled is 25.785282 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [0.000509978,-0.0286269,-0.0460846,0.166055,0.663123],[ -0.00717302 -0.135132 0.218538 1 0; 0.176546 -0.14434 0.215607 -0.156694 1; -0.909709 0.15921 1 0 0; 1 0 0 0 0; -0.226633 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | 0.0395577 | -0.0393684 | 6.9231e-05 |
| 0 | -0 | 0 | 0.000249312 |
| 0.000509978 | 0.038057 | -0.0383952 | 0.00037177 |
| -0.0286269 | 0.0967856 | -0.0772925 | 0.000190132 |
| -0.0460846 | 0.0456412 | -0.0437083 | -0.000624725 |
| 0.166055 | 0.0972051 | -0.253405 | -0.0016674 |
| 0.663123 | -0.335517 | 0.0618402 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000000 699840.000000 -933120.000000 699840.000000 -279936.000000 68358.212192 -21702.212192 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -4.48948e-08 | -2.71057e-09 | -0 | -0 | -0 | -0 | -0 |
| -180.867 | -9.91124 | 0.0940733 | -0.178432 | -0.0285419 | 0.00341056 | 0.00200248 |
| 9021.76 | 543.997 | 18.9058 | 17.3024 | 4.03154 | 0.514674 | 0.0504127 |
| 14636.2 | 873.504 | 30.3711 | 27.5882 | 6.2395 | 0.821128 | 0.114741 |
| -52006.4 | -3158.91 | -101.738 | -99.8131 | -24.2673 | -2.82857 | 0.00408712 |
| -209205 | -12613.8 | -416.542 | -398.829 | -95.4006 | -11.6771 | -0.28631 |
| -314953 | -19016.8 | -632.83 | -599.51 | -141.336 | -18.0028 | -0.638317 |
Method 27.1762, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | -0 | 0 | -0 | 0 | -0 | -0 |
| 0.000799334 | 0.25 | 0 | -0 | 0 | -0 | -0 |
| -2.2911 | 1.13372 | 0.25 | -0 | 0 | -0 | -0 |
| -6.39884 | 2.23834 | 0.591973 | 0.25 | 0 | -0 | -0 |
| -10.4574 | 5.2896 | -1.05581 | 0.690131 | 0.25 | -0 | -0 |
| -15.8285 | 9.36315 | -3.23538 | 1.33087 | 0.191931 | 0.25 | -0 |
| -7.71157 | -16.9548 | 9.3636 | -15.1807 | 27.02 | -10.3391 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | 0.082534 | -0.055822 | -0.0463629 | -0.0247062 | -0.01132 | -0.00480171 |
| 1 | 1.40738 | 0.00788509 | -0.249483 | -0.188031 | -0.108019 | -0.0574754 |
| 1 | 3.98519 | 0.159856 | -0.693894 | -0.607861 | -0.4137 | -0.271065 |
| 1 | 6.11684 | 0.372825 | -0.962193 | -0.976466 | -0.838782 | -0.737781 |
| 1 | 8.92793 | 0.675065 | -1.29983 | -1.49794 | -1.53309 | -1.62669 |
| 1 | 14.5526 | 0.895892 | -5.51196 | -5.22521 | -0.563497 | 7.04562 |
|
| -7.71157 | -16.9548 | 9.3636 | -15.1807 | 27.02 | -10.3391 | 0.25 |
| -0 | 0 | -0 | 0 | 0 | 0 | 1 |
| 27.1762 | 12.3888 | -22.6638 | -19.4558 | 22.0165 | -3.16652 | 0.133755 |
| -14.2869 | -4.0549 | 25.5405 | -0.915005 | -25.6163 | 12.6261 | 0.38419 |
| -4.88553 | -1.87177 | 5.32581 | 10.562 | -21.4772 | 9.28405 | -0.0337144 |
| -7.51327 | 10.3667 | -8.8784 | 8.23578 | -7.79101 | 3.08892 | -0.0970081 |
| 0.254214 | 2.25066 | -3.53962 | 0.499856 | 1.04122 | -0.266045 | -0.057082 |
|
| 1 | 14.5526 | 0.895892 | -5.51196 | -5.22521 | -0.563497 | 7.04562 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -16.429 | 1.65837 | 2.77529 | -0.781012 | -2.49529 | -0.595904 |
| 0 | 6.32234 | -0.181663 | -0.0567523 | 0.435293 | -0.0560819 | -0.248843 |
| 0 | 3.09629 | 0.762439 | -0.052938 | -1.0988 | -1.42612 | 1.99119 |
| 0 | 2.58829 | 0.491845 | 0.103835 | -0.651299 | -1.1439 | 1.74197 |
| 0 | -0.183194 | 0.198865 | 0.0170185 | -0.278464 | -0.422477 | 0.641077 |
|
Maximum coefficient scaled is 27.176160 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [-0.0227043,0.00751299,-0.0610095,-0.0511229,0.0332422],[ 0.0207696 1 0 0 0; -0.00808677 -0.157209 0.357877 1 0; 0.129536 -0.410448 -0.239893 0.761313 1; 0.407102 0.996502 1 0 0; 1 0 0 0 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | -0.000476086 | 0.000665344 | 0.000620533 |
| -0 | 0 | -0 | 0.000642664 |
| -0.0227043 | 0.0506848 | -0.04993 | 0.000113479 |
| 0.00751299 | -0.0137934 | -0.00916058 | -0.00101042 |
| -0.0610095 | 0.224558 | -0.215016 | -0.00276358 |
| -0.0511229 | 0.64376 | -0.70307 | -0.00525266 |
| 0.0332422 | 1.57044 | -1.62267 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000000 699840.000000 -933120.000000 699840.000000 -279936.000000 45084.674987 1571.325013 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 1.00041e-08 | -0 | -2.04143e-10 | -0 | -0 | -0 | -0 |
| 5489.91 | -1.51331 | -111.572 | -13.1615 | -0.887546 | -0.138356 | -0.0398691 |
| -1789.58 | 0.504542 | 37.1693 | 4.44251 | 0.277129 | 0.0431613 | 0.0159707 |
| 14914.7 | 0.626506 | -302.507 | -36.2907 | -2.55843 | -0.300959 | -0.0479052 |
| 12746.1 | 22.3691 | -251.232 | -32.7455 | -3.04873 | -0.0174778 | 0.24231 |
| -8218 | 76.2351 | 166.754 | 10.8211 | -1.29626 | 0.841225 | 1.04399 |
| -243248 | 139.696 | 4954.9 | 576.826 | 37.2599 | 6.02091 | 2.84216 |
Method 29.8209, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | -0 | -0 | 0 | 0 | -0 | 0 |
| -0.021125 | 0.25 | -0 | 0 | 0 | -0 | 0 |
| 0.616954 | -0.251555 | 0.25 | 0 | 0 | -0 | 0 |
| 1.19543 | -2.77662 | 1.24358 | 0.25 | 0 | -0 | 0 |
| 1.94604 | -4.35449 | 2.08488 | -0.100649 | 0.25 | -0 | 0 |
| 0.441878 | -9.11262 | 5.28503 | -1.3444 | 0.738216 | 0.25 | 0 |
| -14.4065 | 9.06265 | 7.42704 | -8.57274 | -0.640803 | 2.04627 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | 0.104458 | -0.0485139 | -0.0445359 | -0.0243002 | -0.0112354 | -0.0047848 |
| 1 | -0.115399 | -0.037948 | -0.0300612 | -0.0366577 | -0.0337271 | -0.0255148 |
| 1 | 0.754278 | 0.320138 | -0.143798 | -0.33134 | -0.33706 | -0.275274 |
| 1 | 1.00755 | 0.581406 | -0.0822656 | -0.410531 | -0.49177 | -0.473291 |
| 1 | 4.74189 | 1.70493 | -0.458474 | -1.41615 | -1.793 | -1.98407 |
| 1 | 5.83408 | 0.239153 | -0.514094 | -1.33079 | -3.29408 | -6.06416 |
|
| -14.4065 | 9.06265 | 7.42704 | -8.57274 | -0.640803 | 2.04627 | 0.25 |
| 0 | 0 | 0 | 0 | -0 | 0 | 1 |
| 4.97581 | 18.234 | -27.291 | -2.63201 | 15.0677 | -4.80097 | 1.05194 |
| -14.9955 | 28.5119 | -0.132076 | -28.5356 | 13.215 | 1.1824 | -0.159641 |
| -8.68284 | -7.89317 | 29.8209 | -19.4757 | -3.09052 | 5.06411 | -0.370657 |
| 7.70934 | -13.2653 | 4.3052 | 2.64961 | -1.45191 | 0.178089 | 0.219762 |
| 2.58117 | -2.33453 | -1.37035 | 1.72772 | 0.164564 | -0.347252 | 0.0864246 |
|
| 1 | 5.83408 | 0.239153 | -0.514094 | -1.33079 | -3.29408 | -6.06416 |
| 0 | -0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -4.6055 | 0.370899 | 0.340896 | 0.0885149 | 2.39601 | 7.90445 |
| 0 | 0.913646 | 0.0997115 | 0.292769 | -0.741483 | -0.456113 | 3.87767 |
| 0 | 4.62785 | 0.0670263 | -0.685242 | -1.11782 | -0.578239 | 4.28974 |
| 0 | -0.344804 | 0.059885 | -1.15113 | -1.70091 | -0.661478 | 4.53469 |
| 0 | -0.507744 | 0.0100698 | -0.273145 | -0.402063 | -0.23668 | 1.11563 |
|
Maximum coefficient scaled is 29.820922 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [0.00761788,0.0376589,0.0203468,-0.24891,0.173803],[ -0.106814 0.707646 0.0807921 -0.155929 1; 0.0141176 -0.212752 0.00808409 1 0; -0.0266649 1 0 0 0; 0.415928 -0.207022 1 0 0; 1 0 0 0 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | -0.02206 | 0.0222492 | -0.000314895 |
| -0 | -0 | 0 | -0.000463151 |
| 0.00761788 | 0.0564904 | -0.0578144 | -0.000303913 |
| 0.0376589 | -0.045752 | 0.0468246 | 0.000628027 |
| 0.0203468 | 0.071871 | -0.0377485 | 0.00217032 |
| -0.24891 | 0.874884 | -0.811276 | 0.00523037 |
| 0.173803 | 0.525451 | -0.804568 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000000 699840.000000 -933120.000000 699840.000000 -279936.000000 22566.737545 24089.262455 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 4.4094e-10 | 0 | -0 | -0 | -0 | -0 | -0 |
| -264.57 | -17.6433 | 2.92331 | 0.196838 | -0.0627747 | -0.00135468 | 0.00492093 |
| -1256.88 | -88.7538 | 14.1824 | 0.75123 | -0.530542 | -0.0829262 | 0.00909287 |
| -570.976 | -47.3103 | 4.76348 | -0.611787 | -0.389974 | 0.080728 | 0.0823651 |
| 8302.34 | 592.198 | -114.827 | -14.6951 | 2.69446 | 1.51747 | 0.51892 |
| -6191.61 | -407.371 | 31.3258 | -7.73932 | -3.76338 | 0.58378 | 1.04287 |
| -33521 | -2364.73 | 368.827 | 24.8706 | -13.4825 | -3.0601 | 0.79445 |
Method 31.0426, c=[
0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1, 1]
AUBV (scaled)
| 0.25 | -0 | 0 | 0 | 0 | -0 | -0 |
| 0.0068585 | 0.25 | -0 | -0 | -0 | 0 | 0 |
| 0.032356 | 0.196464 | 0.25 | -0 | -0 | 0 | 0 |
| -9.64634 | 8.4694 | -2.21646 | 0.25 | -1.0369e-10 | 0 | 0 |
| -9.15978 | 7.9766 | -0.208899 | -0.600462 | 0.25 | 1.2119e-10 | 0 |
| -13.3194 | -8.98687 | 5.22394 | 12.2901 | -6.51525 | 0.25 | 0 |
| 18.1849 | 20.1113 | 2.23183 | -26.1558 | 12.1571 | -0.193186 | 0.25 |
|
| 1 | -0.0833333 | -0.0555556 | -0.0162037 | -0.00385802 | -0.000835905 | -0.000171468 |
| 1 | 0.0764748 | -0.0578417 | -0.0468678 | -0.0248184 | -0.0113433 | -0.00480639 |
| 1 | 0.0211797 | -0.141762 | -0.130684 | -0.092205 | -0.0591273 | -0.0361259 |
| 1 | 3.81007 | -0.103247 | -0.393962 | -0.0666243 | 0.0918315 | 0.10417 |
| 1 | 2.57587 | -0.977183 | -0.880392 | -0.292436 | 0.00034695 | 0.055804 |
| 1 | 12.0575 | 0.179043 | -2.37575 | -0.518376 | 2.29528 | 4.75199 |
| 1 | -25.5861 | -6.20206 | 0.483621 | -0.801337 | -4.7742 | -8.91761 |
|
| 18.1849 | 20.1113 | 2.23183 | -26.1558 | 12.1571 | -0.193186 | 0.25 |
| -0 | 0 | -0 | 0 | 0 | 0 | 1 |
| 20.5431 | -24.8249 | -0.158089 | 21.2702 | -20.1124 | 4.79576 | 2.98851 |
| 16.9786 | -21.5972 | 7.91093 | 12.1719 | -18.9838 | 5.48082 | 2.77038 |
| -28.9543 | 31.0426 | -8.62907 | 0.182057 | -7.06755 | 3.03792 | 1.37634 |
| -21.4585 | 23.0459 | -6.9986 | -1.30395 | -1.19003 | 0.856405 | 0.363623 |
| -5.18797 | 6.19583 | -2.28861 | -0.372338 | 0.0117446 | 0.126341 | 0.0502285 |
|
| 1 | -25.5861 | -6.20206 | 0.483621 | -0.801337 | -4.7742 | -8.91761 |
| 0 | 0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -4.5022 | 0.452186 | -0.13061 | -0.413303 | 0.0699804 | 0.611441 |
| 0 | -4.73164 | -0.264332 | -0.58232 | -0.557168 | 1.29275 | 5.68725 |
| 0 | 9.01202 | 0.293429 | -0.224334 | -0.260924 | 0.682705 | 6.28613 |
| 0 | 6.68521 | 0.0694614 | -0.0870431 | -0.0975042 | -0.0955349 | 3.33936 |
| 0 | 1.46477 | 0.0111177 | 0.025787 | 0.0303043 | -0.190676 | 0.486593 |
|
Maximum coefficient scaled is 31.042593 .
irks(0.25,[0.166667,0.333333,0.5,0.666667,0.833333,1,1], [-0.0136668,0.0503653,0.231284,0.611745,0.956561],[ 0.0390312 0.02866 0.506969 -0.858698 1; -0.434427 0.217343 -0.710884 1 0; 1 0 0 0 0; -0.61947 1 0 0 0; -0.878862 0.47466 1 0 0; ])
[alpha,beta,gamma,stageerror]
| 9.94001e-05 | -0.09298 | 0.0931692 | 0.000201941 |
| -0 | 0 | -0 | -0.000301932 |
| -0.0136668 | 0.0360426 | -0.0229694 | -0.00137051 |
| 0.0503653 | -0.0646733 | 0.00282893 | -0.0026236 |
| 0.231284 | -0.128603 | -0.0422686 | -0.00345305 |
| 0.611745 | -0.360588 | 0.00669954 | -0.00685997 |
| 0.956561 | -0.462097 | 0.158833 | 9.94001e-05 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-279936.000000 699840.000000 -933120.000000 699840.000000 -279936.000000 21005.629963 25650.370037 ] phi0=46656.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 9.73415e-08 | -2.47612e-08 | -6.70586e-09 | -3.45723e-10 | 0 | 0 | 0 |
| 1152.28 | -292.268 | -79.5054 | -4.25028 | 1.05269 | 0.311775 | 0.0507509 |
| -4307.98 | 1077.95 | 292.253 | 15.397 | -3.81048 | -1.09531 | -0.169604 |
| -19436.1 | 4957.23 | 1343.84 | 71.0838 | -17.6585 | -5.03789 | -0.752229 |
| -51178.3 | 13106.7 | 3555.08 | 188.219 | -47.1633 | -13.3229 | -1.86155 |
| -80225.2 | 20491.9 | 5564.75 | 295.982 | -74.742 | -21.2161 | -2.64923 |
| -84970.8 | 21418.3 | 5814.22 | 308.473 | -76.9401 | -22.6883 | -2.68904 |