Method quarters_and_small, c=[
0.25 , 0.5, 0.75, 1]
AUBV (scaled)
| 0.225 | 0 | -0 | 0 |
| 0.211287 | 0.225 | -0 | -0 |
| 0.946338 | -0.342943 | 0.225 | -0 |
| 0.52149 | -0.662474 | 0.490476 | 0.225 |
|
| 1 | 0.025 | -0.05 | -0.0265625 |
| 1 | 0.063713 | -0.0806435 | -0.0833663 |
| 1 | -0.0783954 | 0.0947737 | 0.121956 |
| 1 | 0.425507 | 0.216014 | -0.103603 |
|
| 0.52149 | -0.662474 | 0.490476 | 0.225 |
| 0 | 0 | 0 | 1 |
| -0.0423385 | 0.695379 | -0.784079 | 1.0116 |
| 0.077564 | 0.246379 | -0.321806 | 0.274145 |
|
| 1 | 0.425507 | 0.216014 | -0.103603 |
| 0 | 0 | 0 | 0 |
| 0 | -0.880558 | -0.521284 | 0.774748 |
| 0 | -0.276282 | -0.350743 | 0.521284 |
|
Maximum coefficient scaled is 1.011596 .
irks(0.225,[0.25,0.5,0.75,1], [0.3312,1.005],[ 0.49541 1; 1 0; ])
[alpha,beta,gamma,stageerror]
| 0.000542057 | -0.0229588 | 0.0246866 | -0.0131524 |
| 0 | -0 | 0 | -0.029952 |
| 0.3312 | -0.253506 | -0.0793501 | 0.0381657 |
| 1.005 | -0.595887 | -0.0829382 | 0.000542057 |
Error estimation
phi=[-64.000000 192.000000 -192.000000 64.000000 ]
phi1=[110.801474 -70.202212 -17.198526 20.299631 ] phi0=-43.700369 gives y^{p+1}(t_n-theta*h) at theta=0.545705
M(infty)
| -0 | -0 | 0 | 0 |
| -25.1015 | -3.34423 | 0.711952 | 0.392097 |
| -72.4823 | -9.61823 | 1.89801 | 1.27806 |
| -70.4722 | -8.52338 | 1.36988 | 1.44622 |
Method thirds_and_small, c=[
0.333333 , 0.666667, 1, 1]
AUBV (scaled)
| 0.225 | -0 | 0 | 0 |
| 0.37915 | 0.225 | -0 | 0 |
| 0.576331 | 0.157279 | 0.225 | -0 |
| 0.740628 | 0.864647 | -0.404278 | 0.225 |
|
| 1 | 0.108333 | -0.0388889 | -0.037963 |
| 1 | 0.0625165 | -0.108322 | -0.130087 |
| 1 | 0.0413899 | -0.0439261 | -0.0768157 |
| 1 | -0.425997 | -0.288058 | 0.138096 |
|
| 0.740628 | 0.864647 | -0.404278 | 0.225 |
| 0 | 0 | 0 | 1 |
| -0.715262 | -0.740829 | 0.350709 | 0.892767 |
| -0.570461 | -0.893763 | 0.381671 | 0.404828 |
|
| 1 | -0.425997 | -0.288058 | 0.138096 |
| 0 | 0 | 0 | 0 |
| 0 | 0.212614 | -0.0223407 | 0.495762 |
| 0 | 0.677725 | -0.00100675 | 0.0223407 |
|
Maximum coefficient scaled is 0.893763 .
irks(0.225,[0.333333,0.666667,1,1], [0.2463,0.5101],[ 1 0; 0.13519 1; ])
[alpha,beta,gamma,stageerror]
| 0.000542057 | 0.0323451 | -0.0306173 | -0.00889114 |
| 0 | -0 | -0 | -0.0296206 |
| 0.2463 | -0.193098 | 0.0674604 | -0.0190979 |
| 0.5101 | -0.163906 | 0.150004 | 0.000542057 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 ]
phi1=[81.000000 -81.000000 86.238349 -59.238349 ] phi0=-27.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | 0 | 0 |
| 7.129 | 2.64342 | -0.351534 | -0.471756 |
| 17.9502 | 5.5179 | -1.04795 | -0.824498 |
| 27.2179 | 10.8232 | -2.09821 | -1.59546 |
Method thirds_uos_optimized, c=[
0.333333 , 0.666667, 1, 1]
AUBV (scaled)
| 0.225 | -0 | -0 | 0 |
| -0.914964 | 0.225 | 0 | -0 |
| -2.12064 | 0.762168 | 0.225 | 0 |
| -0.521521 | 0.241606 | 0.0426627 | 0.225 |
|
| 1 | 0.108333 | -0.0388889 | -0.037963 |
| 1 | 1.35663 | 0.754421 | 0.301284 |
| 1 | 2.13347 | 0.947533 | 0.0156549 |
| 1 | 1.01225 | 0.490214 | 0.0487104 |
|
| -0.521521 | 0.241606 | 0.0426627 | 0.225 |
| 0 | 0 | 0 | 1 |
| -1.49595 | -0.869278 | -0.296596 | 1.90823 |
| -1.02164 | -0.434841 | -0.161988 | 0.779791 |
|
| 1 | 1.01225 | 0.490214 | 0.0487104 |
| 0 | -0 | -0 | -0 |
| 0 | 0.753595 | -0.0669255 | -0.177205 |
| 0 | 0.838679 | 0.0252759 | 0.0669255 |
|
Maximum coefficient scaled is 2.133467 .
irks(0.225,[0.333333,0.666667,1,1], [0.0302,0.5907],[ -0.8826 1; 1 0; ])
[alpha,beta,gamma,stageerror]
| 0.000542057 | 0.000873652 | 0.000854174 | -0.00519916 |
| -0 | 0 | 0 | 0.0438205 |
| 0.0302 | 0.0298328 | -0.0476719 | -0.00453192 |
| 0.5907 | -0.233917 | -0.0848097 | 0.000542057 |
Error estimation
phi=[0.000000 0.000000 0.000000 0.000000 ]
phi1=[81.000000 -81.000000 -779.654975 806.654975 ] phi0=-27.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | -0 | -0 |
| 3.75601 | 0.490133 | -0.07246 | 0.0280001 |
| 49.0182 | 10.9717 | -0.195008 | -0.216153 |
| 74.4644 | 18.4456 | -0.443428 | -0.295125 |