Method maxcoeff=2.9, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | -0 | -0 | 0 | 0 |
| 0.342666 | 0.285714 | -0 | 0 | 0 |
| 0.444812 | -0.149747 | 0.285714 | 0 | 0 |
| -0.0576971 | -0.381502 | 0.278881 | 0.285714 | 0 |
| -1.50952 | 1.2339 | 2.22131 | -1.34199 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | -0.12838 | -0.207047 | -0.153536 | -0.101774 |
| 1 | 0.169221 | 0.0612696 | -0.0313598 | -0.118664 |
| 1 | 0.874603 | 0.4206 | -0.0308104 | -0.419112 |
| 1 | 0.110578 | -0.698562 | -0.222033 | 0.954026 |
|
| -1.50952 | 1.2339 | 2.22131 | -1.34199 | 0.285714 |
| 0 | 0 | 0 | 0 | 1 |
| 2.15407 | -1.41538 | -2.92849 | 1.70108 | 1.05482 |
| 2.2364 | -1.21266 | -2.84084 | 1.58701 | 0.571785 |
| 2.9234 | -0.701302 | -2.02284 | 0.949272 | 0.202843 |
|
| 1 | 0.110578 | -0.698562 | -0.222033 | 0.954026 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | -0.566101 | 0.21928 | 0.331776 | 0.491292 |
| 0 | -0.341701 | 0.0381276 | -0.192298 | 0.625293 |
| 0 | -1.35138 | -0.0303716 | -0.0649675 | -0.0269828 |
|
Maximum coefficient scaled is 2.928490 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.0816,0.232,0.419],[ -0.459002 0.167124 1; 0.539889 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.0495424 | -0.0506454 | -0.00502776 |
| 0 | -0 | -0 | -0.0167004 |
| 0.0816 | -0.110548 | 0.0763574 | -0.00225608 |
| 0.232 | -0.123264 | 0.107656 | 0.00240694 |
| 0.419 | 0.0221207 | 0.0343183 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 6657.919213 -6401.919213 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | 0 | 0 | 0 | 0 |
| -68.9948 | -5.61552 | 1.79631 | 0.266585 | -0.0702156 |
| -194.993 | -16.4748 | 4.60042 | 0.79786 | -0.0572601 |
| -380.894 | -30.325 | 8.39594 | 1.13166 | 0.0525001 |
| -831.65 | -71.5049 | 20.6583 | 2.76525 | -0.116552 |
Method john-24-10-05a, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | 0 | -0 | 0 | 0 |
| 0.546778 | 0.285714 | -0 | 0 | -0 |
| 0.580959 | -0.049954 | 0.285714 | 0 | -0 |
| -0.53723 | -0.724377 | 0.710726 | 0.285714 | -0 |
| 0.598858 | 1.22727 | 1.09563 | -0.942304 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | -0.332493 | -0.309104 | -0.191807 | -0.114531 |
| 1 | -0.0667193 | -0.106597 | -0.131732 | -0.17707 |
| 1 | 1.26517 | 0.355474 | -0.41248 | -0.946443 |
| 1 | -1.26517 | -0.856962 | 0.0881574 | 1.12642 |
|
| 0.598858 | 1.22727 | 1.09563 | -0.942304 | 0.285714 |
| 0 | 0 | 0 | 0 | 1 |
| -0.918648 | -1.26517 | -1.03219 | 0.957838 | 0.993001 |
| -0.548116 | -1.00336 | -1.14261 | 0.904723 | 0.524195 |
| 1.26517 | -0.184502 | -1.26517 | 0.568317 | 0.185666 |
|
| 1 | -1.26517 | -0.856962 | 0.0881574 | 1.12642 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1.26517 | 0.371098 | 0.0104253 | 0.628463 |
| 0 | 1.26517 | 0.133494 | -0.503311 | 0.748417 |
| 0 | -0.569481 | -0.0582987 | -0.225824 | 0.132212 |
|
Maximum coefficient scaled is 1.265166 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.0970762,0.244027,0.420115],[ -0.143543 0.466178 1; 0.257525 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.061909 | -0.063012 | -0.00572628 |
| 0 | -0 | 0 | -0.0253818 |
| 0.0970762 | -0.117423 | 0.07664 | -0.0153849 |
| 0.244027 | -0.0972372 | 0.0917941 | -0.0270568 |
| 0.420115 | 0.184402 | -0.116872 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -653.306743 909.306743 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | 0 | 0 | 0 |
| -66.6807 | -7.60092 | 1.75508 | 0.586124 | 0.0633437 |
| -166.389 | -19.6393 | 3.8998 | 1.52883 | 0.312568 |
| -313.191 | -35.2 | 6.67707 | 2.44212 | 0.761721 |
| -712.956 | -82.1213 | 18.0436 | 5.49828 | 1.259 |
Method john-24-10-05b, c=[
0.2 , 0.4, 0.6, 0.8, 1]
AUBV (scaled)
| 0.285714 | -0 | -0 | 0 | 0 |
| 0.140345 | 0.285714 | -0 | 0 | 0 |
| 0.429729 | -0.135731 | 0.285714 | 0 | 0 |
| -1.0433 | -0.818529 | 0.727581 | 0.285714 | 0 |
| 0.479519 | 1.95193 | 1.95193 | -1.71716 | 0.285714 |
|
| 1 | -0.0857143 | -0.0742857 | -0.0262857 | -0.00754286 |
| 1 | -0.0260593 | -0.124709 | -0.0899843 | -0.0520339 |
| 1 | 0.020288 | -0.0461637 | -0.0789879 | -0.0962613 |
| 1 | 1.64853 | 0.381901 | -0.30427 | -0.561244 |
| 1 | -1.95193 | -0.919634 | 0.337258 | 1.17239 |
|
| 0.479519 | 1.95193 | 1.95193 | -1.71716 | 0.285714 |
| 0 | 0 | 0 | 0 | 1 |
| -0.974861 | -1.70923 | -1.95193 | 1.71045 | 0.97364 |
| -0.729114 | -1.15141 | -1.95193 | 1.50795 | 0.491135 |
| 1.95193 | -0.202145 | -1.88803 | 0.863423 | 0.161868 |
|
| 1 | -1.95193 | -0.919634 | 0.337258 | 1.17239 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1.95193 | 0.415642 | -0.159487 | 0.757665 |
| 0 | 1.83336 | 0.160092 | -0.620423 | 0.95173 |
| 0 | -0.887047 | -0.0586352 | -0.241508 | 0.204781 |
|
Maximum coefficient scaled is 1.951928 .
irks(0.285714,[0.2,0.4,0.6,0.8,1], [0.114196,0.284526,0.472827],[ -0.114162 0.487435 1; 0.295121 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.06659 | -0.067693 | -0.00565306 |
| 0 | -0 | -0 | -0.0126417 |
| 0.114196 | -0.131133 | 0.077138 | -0.00905673 |
| 0.284526 | -0.106794 | 0.0864591 | -0.00881187 |
| 0.472827 | 0.205353 | -0.144393 | -0.000338649 |
Error estimation
phi=[625.000000 -2500.000000 3750.000000 -2500.000000 625.000000 ]
phi1=[-927.120743 604.241486 645.758514 -947.879257 314.575851 ] phi0=310.424149 gives y^{p+1}(t_n-theta*h) at theta=0.499336
M(infty)
| -0 | -0 | 0 | 0 | 0 |
| -134.293 | -10.1976 | 2.74735 | 0.665469 | 0.0681862 |
| -333.325 | -25.9631 | 6.35719 | 1.73867 | 0.334024 |
| -593.492 | -44.6475 | 10.6294 | 2.69871 | 0.798217 |
| -1210.17 | -92.9385 | 24.5237 | 5.27451 | 1.14171 |