Method 1.248, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | 0 | 0 | -0 | -0 |
| 0.466403 | 0.285714 | 0 | -0 | -0 |
| -1.17096 | 0.562674 | 0.285714 | -0 | -0 |
| 1.03394 | 1.24796 | -0.319651 | 0.285714 | -0 |
| -1.09398 | 0.175796 | 0.645269 | -0.260759 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | -0.252117 | -0.268916 | -0.176736 | -0.109507 |
| 1 | 1.07257 | 0.156734 | -0.262719 | -0.373889 |
| 1 | -1.24796 | -0.856879 | -0.447563 | -0.292046 |
| 1 | 1.24796 | 0.353379 | -0.0904835 | -0.208237 |
|
| -1.09398 | 0.175796 | 0.645269 | -0.260759 | 0.285714 |
| 0 | 0 | 0 | 0 | 1 |
| -0.49606 | -0.523734 | -1.24796 | 0.636228 | 1.24796 |
| -0.965386 | -0.501659 | -0.94567 | 0.519451 | 0.645305 |
| -0.311636 | -0.136841 | -0.207827 | 0.121675 | 0.121509 |
|
| 1 | 1.24796 | 0.353379 | -0.0904835 | -0.208237 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0.383566 | -0.12467 | -0.0608165 | 0.862056 |
| 0 | 1.24796 | 0.073344 | -0.341197 | 1.24796 |
| 0 | 0.41312 | 0.118031 | -0.217783 | 0.465868 |
|
Maximum coefficient scaled is 1.247959 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.0983743,0.476535,1.04198],[ 0.332454 -0.161174 1; 1 0 0; 0.859164 1 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | -0.00690079 | 0.00579781 | -0.00761039 |
| 0 | -0 | 0 | -0.0325779 |
| 0.0983743 | -0.107974 | 0.00547073 | -0.032453 |
| 0.476535 | -0.436654 | 0.0384911 | -0.0931488 |
| 1.04198 | -0.659725 | 0.0505471 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -98.064867 354.064867 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | 0 | -0 | -0 | -0 |
| 8.75239 | 2.22698 | -0.0714099 | -0.144139 | -0.0348592 |
| 46.1691 | 11.6117 | -0.588913 | -0.734224 | -0.0966084 |
| 94.4943 | 26.3249 | -1.41278 | -1.82175 | -0.0182414 |
| 81.1722 | 23.9051 | -0.519828 | -2.19546 | 0.183681 |
Method 1.2652, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | 0 | 0 | -0 | -0 |
| 0.546779 | 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],[ -0.143541 0.466188 1; 0.257529 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 -653.306723 909.306723 ] 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 1.2905, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | -0 | 0 | -0 | -0 |
| 0.139784 | 0.285714 | 0 | -0 | -0 |
| 0.608893 | -0.175049 | 0.285714 | -0 | 0 |
| -0.0584026 | -1.24619 | 0.728352 | 0.285714 | 0 |
| -0.0786971 | 1.29053 | 1.29053 | -1.00696 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | 0.0745017 | -0.105606 | -0.115495 | -0.0890936 |
| 1 | 0.0304412 | 0.00453079 | -0.0431487 | -0.116268 |
| 1 | 1.29053 | 0.611437 | -0.140642 | -0.745205 |
| 1 | -0.78111 | -0.744473 | 0.0328418 | 1.06689 |
|
| -0.0786971 | 1.29053 | 1.29053 | -1.00696 | 0.285714 |
| -0 | 0 | 0 | 0 | 1 |
| -1.01395 | -1.29053 | -0.838638 | 0.890205 | 0.96238 |
| -0.704376 | -0.758023 | -1.29053 | 0.944263 | 0.518136 |
| 0.857762 | 0.0691086 | -1.2774 | 0.553086 | 0.174138 |
|
| 1 | -0.78111 | -0.744473 | 0.0328418 | 1.06689 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1.29053 | 0.350289 | 0.0154585 | 0.713498 |
| 0 | 1.29053 | 0.121206 | -0.508842 | 0.751206 |
| 0 | -0.376694 | -0.0363369 | -0.238721 | 0.158553 |
|
Maximum coefficient scaled is 1.290528 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.107689,0.248013,0.458143],[ -0.173352 0.583817 1; 0.245195 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.058885 | -0.059988 | -0.00620002 |
| 0 | -0 | 0 | -0.0126675 |
| 0.107689 | -0.131314 | 0.0819769 | -0.00519154 |
| 0.248013 | -0.106057 | 0.100121 | 0.00296479 |
| 0.458143 | 0.136634 | -0.0985153 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 2385.103862 -2129.103862 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | 0 | 0 | -0 |
| -77.39 | -8.85724 | 2.1247 | 0.735178 | 0.0900613 |
| -176.433 | -20.8417 | 4.37255 | 1.74401 | 0.360972 |
| -349.261 | -39.6076 | 8.06229 | 3.03327 | 0.876096 |
| -742.608 | -85.5007 | 19.682 | 6.27471 | 1.45142 |
Method 1.2823, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | 0 | 0 | -0 | -0 |
| 0.114074 | 0.285714 | 0 | -0 | -0 |
| 1.27145 | -0.4371 | 0.285714 | -0 | -0 |
| 0.0173148 | -1.28231 | 0.696945 | 0.285714 | -0 |
| 0.577421 | 1.28233 | 0.474526 | -0.580367 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | 0.100212 | -0.0927514 | -0.110675 | -0.0874868 |
| 1 | -0.370069 | -0.064699 | 0.0291591 | -0.0266527 |
| 1 | 1.28233 | 0.656802 | -0.0747551 | -0.678881 |
| 1 | -1.03963 | -0.693525 | 0.0131801 | 0.700593 |
|
| 0.577421 | 1.28233 | 0.474526 | -0.580367 | 0.285714 |
| 0 | 0 | 0 | 0 | 1 |
| -0.939412 | -1.26295 | -1.09187 | 0.898026 | 1.1139 |
| -0.593389 | -0.893861 | -1.28229 | 0.863756 | 0.623467 |
| 1.28232 | -0.441576 | -0.946001 | 0.437796 | 0.204075 |
|
| 1 | -1.03963 | -0.693525 | 0.0131801 | 0.700593 |
| 0 | -0 | -0 | -0 | -0 |
| 0 | 1.28231 | 0.346619 | -0.0698812 | 0.485032 |
| 0 | 1.28231 | 0.139538 | -0.516155 | 0.698984 |
| 0 | -0.536617 | -0.064326 | -0.23849 | 0.169536 |
|
Maximum coefficient scaled is 1.282331 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.0742145,0.236636,0.478059],[ -0.0992709 0.43704 1; 0.258039 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.034503 | -0.0356059 | -0.00479467 |
| -0 | 0 | 0 | -0.0100515 |
| 0.0742145 | -0.0830839 | 0.047605 | -0.00263955 |
| 0.236636 | -0.094005 | 0.0550934 | -0.00152203 |
| 0.478059 | 0.114135 | -0.106039 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -6686.942298 6942.942298 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | 0 | 0 | 0 |
| -71.4437 | -8.43431 | 1.38528 | 0.491576 | 0.0631379 |
| -228.285 | -27.5798 | 3.97516 | 1.61328 | 0.334911 |
| -489.61 | -57.335 | 8.11951 | 3.0757 | 0.863355 |
| -997.222 | -118.318 | 18.9798 | 6.07909 | 1.38346 |
Method 1.4082, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.285714 | 0 | 0 | -0 | -0 |
| 0.595828 | 0.285714 | 0 | -0 | -0 |
| 1.23816 | -0.560583 | 0.285714 | -0 | -0 |
| 1.4082 | -1.05124 | 0.410691 | 0.285714 | -0 |
| 0.855696 | 0.208229 | 0.232303 | -0.190998 | 0.285714 |
|
| 1 | -0.0357143 | -0.0803571 | -0.0379464 | -0.0139509 |
| 1 | -0.381542 | -0.333628 | -0.201003 | -0.117596 |
| 1 | -0.213296 | 0.0754295 | 0.128014 | 0.0371698 |
| 1 | -0.0533669 | 0.159674 | -0.0257922 | -0.398291 |
| 1 | -0.390944 | -0.173964 | 0.00722437 | 0.071527 |
|
| 0.855696 | 0.208229 | 0.232303 | -0.190998 | 0.285714 |
| -0 | 0 | 0 | 0 | 1 |
| -0.447416 | -0.806062 | -1.34436 | 0.643539 | 1.40813 |
| 0.435082 | -0.864344 | -1.36237 | 0.593203 | 0.827102 |
| 0.275298 | -0.238706 | -0.35342 | 0.145047 | 0.166524 |
|
| 1 | -0.390944 | -0.173964 | 0.00722437 | 0.071527 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0.546169 | -0.0570252 | -0.197956 | 0.492937 |
| 0 | 0.371328 | -0.15025 | -0.395233 | 1.02276 |
| 0 | 0.00525628 | 0.00804428 | -0.210906 | 0.452258 |
|
Maximum coefficient scaled is 1.408201 .
irks(0.285714,[0.25,0.5,0.75,1,1], [0.048881,0.349889,0.955997],[ 0.0883338 0.130203 1; 0.5462 1 0; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | 0.00153946 | -0.00264244 | -0.00477088 |
| 0 | -0 | -0 | -0.0251404 |
| 0.048881 | -0.038413 | -0.00831707 | 0.0102584 |
| 0.349889 | -0.254108 | -0.0315039 | -0.0199442 |
| 0.955997 | -0.528416 | -0.0356257 | -0.000338649 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -2260.659501 2516.659501 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | 0 | 0 | 0 | 0 |
| -11.1707 | -1.53696 | 0.0399141 | 0.0448629 | 0.0182737 |
| -85.5504 | -11.0441 | 0.362793 | 0.282782 | 0.142569 |
| -239.709 | -28.8475 | 1.22752 | 0.526279 | 0.477477 |
| -250.875 | -30.2763 | 2.16648 | 0.077428 | 0.647886 |