Method 2/7, c=[1:5]/5, c=[
0.2 , 0.4, 0.6, 0.8, 1]
AUBV (scaled)
| 0.285714 | -0 | -0 | 0 | 0 |
| 1.00871 | 0.285714 | -0 | 0 | 0 |
| 0.838377 | -0.623507 | 0.285714 | 0 | 0 |
| 0.534633 | -1.36839 | 0.865148 | 0.285714 | 0 |
| 1.65269 | 0.064244 | 0.0410898 | -0.11014 | 0.285714 |
|
| 1 | -0.0857143 | -0.0742857 | -0.0262857 | -0.00754286 |
| 1 | -0.894419 | -0.472053 | -0.194187 | -0.0798214 |
| 1 | 0.0994157 | 0.180598 | 0.106107 | 0.0155326 |
| 1 | 0.482893 | 0.0255367 | -0.378261 | -0.589832 |
| 1 | -0.933598 | -0.156983 | 0.0807897 | -0.0221239 |
|
| 1.65269 | 0.064244 | 0.0410898 | -0.11014 | 0.285714 |
| -0 | 0 | 0 | 0 | 1 |
| -0.765028 | -1.37189 | -1.83607 | 0.59176 | 1.66878 |
| 0.740399 | -1.60666 | -1.99444 | 0.574933 | 1.09792 |
| 0.802149 | -0.598638 | -0.665941 | 0.175299 | 0.276272 |
|
| 1 | -0.933598 | -0.156983 | 0.0807897 | -0.0221239 |
| 0 | 0 | -0 | -0 | -0 |
| 0 | 1.71244 | 0.322432 | -0.409247 | 0.0750166 |
| 0 | 1.18785 | 0.266764 | -0.561287 | 0.541664 |
| 0 | 0.0108596 | 0.124158 | -0.255085 | 0.238856 |
|
Maximum coefficient scaled is 1.994444 .
irks(0.285714,[0.2,0.4,0.6,0.8,1], [0.007,0.2195,0.7078],[ 0.208402 1 0; 0.5384 -0.156521 1; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000338649 | -0.00332691 | 0.00222392 | -0.00146045 |
| -0 | 0 | 0 | -0.011397 |
| 0.007 | 0.0225358 | -0.0274904 | 0.00468624 |
| 0.2195 | -0.0753767 | -0.0729854 | -0.0365371 |
| 0.7078 | -0.20039 | -0.0810911 | -0.000338649 |
Error estimation
phi=[625.000000 -2500.000000 3750.000000 -2500.000000 625.000000 ]
phi1=[-1403.782854 1557.565708 -307.565708 -471.217146 219.243429 ] phi0=405.756571 gives y^{p+1}(t_n-theta*h) at theta=0.529842
M(infty)
| -0 | -0 | -0 | -0 | -0 |
| -1.93537 | -0.293254 | -0.128915 | 0.00499577 | 0.0268137 |
| -160.955 | -18.5059 | -0.326103 | 0.0960436 | 0.133141 |
| -541.738 | -60.7647 | -0.261964 | 0.111895 | 0.403655 |
| -765.751 | -87.9551 | 1.07145 | -0.179374 | 0.507462 |
Method 1/3, c=[1:4,4]/4, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.333333 | 0 | 0 | -0 | -0 |
| 1.24628 | 0.333333 | 0 | -0 | -0 |
| -1.16851 | 0.748886 | 0.333333 | -0 | -0 |
| 1.12614 | 1.14952 | -0.16717 | 0.333333 | -0 |
| -1.20995 | 0.232372 | 0.725225 | -0.35023 | 0.333333 |
|
| 1 | -0.0833333 | -0.104167 | -0.046875 | -0.0169271 |
| 1 | -1.07961 | -0.706474 | -0.358678 | -0.182059 |
| 1 | 0.83629 | -0.102131 | -0.483194 | -0.547505 |
| 1 | -1.44182 | -1.1285 | -0.791195 | -0.69638 |
| 1 | 1.26925 | 0.318558 | -0.120542 | -0.196796 |
|
| -1.20995 | 0.232372 | 0.725225 | -0.35023 | 0.333333 |
| 0 | 0 | 0 | 0 | 1 |
| -0.766962 | -0.217732 | -1.33262 | 0.735664 | 1.13942 |
| -1.30299 | -0.149677 | -0.999015 | 0.574642 | 0.55666 |
| -0.392946 | -0.0326485 | -0.212162 | 0.125944 | 0.0983984 |
|
| 1 | 1.26925 | 0.318558 | -0.120542 | -0.196796 |
| 0 | -0 | -0 | -0 | -0 |
| 0 | 0.442223 | -0.150038 | -0.0693689 | 0.905241 |
| 0 | 1.32038 | 0.0370903 | -0.351499 | 1.31691 |
| 0 | 0.413414 | 0.0986797 | -0.21684 | 0.501538 |
|
Maximum coefficient scaled is 1.441824 .
irks(0.333333,[0.25,0.5,0.75,1,1], [0.101791,0.49354,1.08097],[ 0.327103 -0.173002 1; 1 0 0; 0.957083 1 0; ])
[alpha,beta,gamma,stageerror]
| -0.00349794 | -0.00282711 | -0.00418592 | -0.00996589 |
| -0 | 0 | -0 | -0.0744703 |
| 0.101791 | -0.111965 | 0.00193302 | -0.0737807 |
| 0.49354 | -0.456166 | 0.0244553 | -0.16041 |
| 1.08097 | -0.706997 | 0.0320444 | -0.00349794 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -188.164236 444.164236 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | -0 | 0 | 0 |
| 10.8287 | 2.02849 | -0.135483 | -0.112517 | -0.0179875 |
| 56.1379 | 10.6741 | -0.896288 | -0.582083 | -0.0149505 |
| 115.525 | 24.3191 | -2.06057 | -1.49444 | 0.156965 |
| 97.6935 | 21.4021 | -1.10384 | -1.84648 | 0.36224 |
Method 2/3, c=[1:4,4]/4, c=[
0.25 , 0.5, 0.75, 1, 1]
AUBV (scaled)
| 0.666667 | 0 | -0 | 0 | 0 |
| 1.46522 | 0.666667 | -0 | 0 | 0 |
| -1.39516 | 1.33872 | 0.666667 | -0 | 0 |
| 0.62114 | 1.58061 | -0.550453 | 0.666667 | -0 |
| 0.473052 | -0.1951 | 1.44568 | -0.629146 | 0.666667 |
|
| 1 | -0.416667 | -0.270833 | -0.109375 | -0.0377604 |
| 1 | -1.63189 | -1.14928 | -0.649729 | -0.36241 |
| 1 | 0.139775 | -1.07864 | -1.44557 | -1.39076 |
| 1 | -1.31797 | -1.39884 | -1.37303 | -1.56691 |
| 1 | -0.761153 | -1.28499 | -1.49452 | -1.52168 |
|
| 0.473052 | -0.1951 | 1.44568 | -0.629146 | 0.666667 |
| 0 | 0 | 0 | 0 | 1 |
| -1.34193 | -1.65766 | -1.2399 | 1.51147 | 0.978375 |
| -0.756668 | -0.836797 | -0.556521 | 0.733883 | 0.351793 |
| -0.0862237 | -0.254637 | -0.109691 | 0.176147 | 0.0683961 |
|
| 1 | -0.761153 | -1.28499 | -1.49452 | -1.52168 |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1.74964 | 0.208787 | -0.88234 | -0.954337 |
| 0 | 1.06431 | -0.121439 | -0.548426 | 1.06212 |
| 0 | 0.206009 | -0.0268006 | -0.341381 | 0.339638 |
|
Maximum coefficient scaled is 1.749644 .
irks(0.666667,[0.25,0.5,0.75,1,1], [-0.1855,0.3348,0.6192],[ 0.549108 1 0; 0.119393 -0.845693 1; 1 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.0153292 | -0.155042 | 0.131054 | 0.0179421 |
| 0 | 0 | 0 | 0.0592762 |
| -0.1855 | 0.316013 | -0.201151 | -0.0265714 |
| 0.3348 | -0.207543 | -0.185266 | -0.00370414 |
| 0.6192 | 0.0310104 | -0.079619 | -0.0153292 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 0.000000 ]
phi1=[-1024.000000 1536.000000 -1024.000000 -8254.593846 8510.593846 ] phi0=256.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | 0 | -0 | -0 | -0 |
| 7.43116 | 1.39621 | 0.267707 | 0.159011 | 0.0709087 |
| -0.710586 | -2.50743 | -1.56243 | -0.164998 | 0.160139 |
| -8.1804 | -4.28522 | -3.24088 | -0.456605 | 0.572869 |
| -21.1961 | -6.40118 | -3.02868 | -1.28592 | 0.622826 |
Method 1/5,c=[1:5,5]/5, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
| 0.2 | -0 | 0 | 0 | -0 | 0 |
| -0.0266025 | 0.2 | 0 | 0 | -0 | 0 |
| -0.849203 | 0.369105 | 0.2 | 0 | -0 | 0 |
| 0.482847 | 1.80236 | -1.33965 | 0.2 | -0 | 0 |
| -0.621923 | 1.76319 | -1.1883 | 0.103302 | 0.2 | 0 |
| 2.29114 | 2.19461 | -2.64281 | -0.757682 | 0.860273 | 0.2 |
|
| 1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
| 1 | 0.226603 | 0.010641 | -0.0288077 | -0.0247487 | -0.0151472 |
| 1 | 0.880098 | 0.164397 | -0.0752661 | -0.110516 | -0.0922918 |
| 1 | -0.345549 | 0.292561 | 0.651754 | 0.680607 | 0.551612 |
| 1 | 0.743728 | 0.698892 | 0.713323 | 0.583654 | 0.337743 |
| 1 | -1.14553 | 0.590976 | 0.799819 | -0.0411057 | -1.33633 |
|
| 2.29114 | 2.19461 | -2.64281 | -0.757682 | 0.860273 | 0.2 |
| -0 | 0 | 0 | -0 | 0 | 1 |
| 2.3854 | -0.413744 | -2.76879 | -2.35975 | 2.97547 | 0.333952 |
| 2.71043 | 2.2512 | -2.20325 | -2.93099 | 2.3927 | 0.583776 |
| -0.274976 | 1.78542 | 0.801515 | -0.750123 | -0.205354 | 0.738782 |
| -0.428573 | -0.433322 | 1.26278 | 0.291219 | -0.61533 | 0.302099 |
|
| 1 | -1.14553 | 0.590976 | 0.799819 | -0.0411057 | -1.33633 |
| 0 | -0 | -0 | -0 | -0 | -0 |
| 0 | -0.152527 | 0.856151 | 0.505107 | 0.0169109 | 0.11372 |
| 0 | -2.80387 | -1.50461 | -1.32826 | -0.662689 | 2.23813 |
| 0 | -2.09527 | -2.14683 | -1.84969 | -0.738241 | 3.12339 |
| 0 | -0.378876 | -0.836741 | -0.723829 | -0.30989 | 1.21035 |
|
Maximum coefficient scaled is 3.123392 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0239,-0.0009,-0.0012,0.2891],[ -0.0745374 0.0747907 1 0; 0.36985 -0.362302 0.194616 1; -0.259373 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
| -0.000133778 | -0.0131155 | 0.012924 | -0.000478888 |
| -0 | -0 | 0 | 8.49198e-05 |
| 0.0239 | -0.0353553 | 0.0284458 | 0.00166498 |
| -0.0009 | 0.0867007 | -0.0625405 | 0.0052242 |
| -0.0012 | 0.640776 | -0.641329 | 0.00909062 |
| 0.2891 | 1.1035 | -1.18828 | -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 4352.787388 -1227.787388 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | -0 | -0 | -0 | -0 | -0 |
| -103.026 | -1.52814 | -0.864777 | -0.596911 | -0.015114 | 0.0393975 |
| -12.9551 | -4.42405 | -1.28936 | -0.143141 | 0.112547 | 0.0718653 |
| -45.1288 | -25.6422 | -7.34689 | -0.7082 | 0.625532 | 0.424545 |
| -1288.01 | -79.0454 | -26.9738 | -8.78687 | 1.0046 | 1.56393 |
| -4297.97 | -99.7613 | -43.2279 | -25.0343 | -0.71169 | 2.5211 |