Method c=[1/3,2/3,1],beta=0.3385, c=[
0.333333 , 0.666667, 1]
AUBV (scaled)
| 0.444444 | 0 | -0 |
| 1.03744 | 0.444444 | 0 |
| 0.7671 | -0.381171 | 0.444444 |
|
| 1 | -0.111111 | -0.185185 |
| 1 | -0.815215 | -0.839773 |
| 1 | 0.169626 | 0.107939 |
|
| 0.7671 | -0.381171 | 0.444444 |
| 0 | 0 | 1 |
| -1.03766 | 0.310905 | 0.638615 |
|
| 1 | 0.169626 | 0.107939 |
| 0 | -0 | -0 |
| 0 | 0.0881351 | 0 |
|
Maximum coefficient scaled is 1.037655 .
irks(0.444444,[0.333333,0.666667,1], [0.3385],[ 1; ])
[alpha,beta,gamma,stageerror]
| 0.0048011 | -0.0220577 | 0.0564084 | -0.0498611 |
| -0 | 0 | -0 | -0.24915 |
| 0.3385 | -0.0692678 | -0.0453145 | 0.0048011 |
Error estimation
phi=[9.000000 -18.000000 9.000000 ]
phi1=[-11.305520 2.305520 2.231493 ] phi0=6.768507 gives y^{p+1}(t_n-theta*h) at theta=0.584019
M(infty)
| -0 | -0 | 0 |
| 4.20809 | 0.25947 | -0.0878305 |
| 11.9108 | 0.766528 | -0.25947 |
Method c=[1/3,2/3,1],beta=1/3, c=[
0.333333 , 0.666667, 1]
AUBV (scaled)
| 0.444444 | 0 | -0 |
| 1.02058 | 0.444444 | 0 |
| 0.786008 | -0.388889 | 0.444444 |
|
| 1 | -0.111111 | -0.185185 |
| 1 | -0.798354 | -0.828532 |
| 1 | 0.158436 | 0.105624 |
|
| 0.786008 | -0.388889 | 0.444444 |
| 0 | 0 | 1 |
| -1.07143 | 0.321429 | 0.642857 |
|
| 1 | 0.158436 | 0.105624 |
| 0 | 0 | 0 |
| 0 | 0.107143 | 0 |
|
Maximum coefficient scaled is 1.071429 .
irks(0.444444,[0.333333,0.666667,1], [0.333333],[ 1; ])
[alpha,beta,gamma,stageerror]
| 0.0048011 | -0.0215478 | 0.0558985 | -0.0493827 |
| 0 | -0 | -0 | -0.24417 |
| 0.333333 | -0.0661376 | -0.0449735 | 0.0048011 |
Error estimation
phi=[9.000000 -18.000000 9.000000 ]
phi1=[-11.336438 2.336438 2.221187 ] phi0=6.778813 gives y^{p+1}(t_n-theta*h) at theta=0.584400
M(infty)
| 0 | 0 | 0 |
| 4.28125 | 0.270833 | -0.0902778 |
| 12.2009 | 0.8125 | -0.270833 |
Method c=[1/3,2/3,1],beta=0.0424375, c=[
0.333333 , 0.666667, 1]
AUBV (scaled)
| 0.444444 | -0 | 0 |
| 2.62034 | 0.444444 | 0 |
| -0.0172538 | -0.22672 | 0.444444 |
|
| 1 | -0.111111 | -0.185185 |
| 1 | -2.39812 | -1.89504 |
| 1 | 0.799529 | 0.424906 |
|
| -0.0172538 | -0.22672 | 0.444444 |
| 0 | 0 | 1 |
| -2.53723 | 0.478202 | 1.02694 |
|
| 1 | 0.799529 | 0.424906 |
| 0 | 0 | 0 |
| 0 | 1.03209 | 0 |
|
Maximum coefficient scaled is 2.620339 .
irks(0.444444,[0.333333,0.666667,1], [0.0424375],[ 1; ])
[alpha,beta,gamma,stageerror]
| 0.0048011 | 6.91109e-07 | 0.03435 | -0.0224479 |
| 0 | -0 | 0 | -0.235167 |
| 0.0424375 | 0.0993422 | -0.101143 | 0.0048011 |
Error estimation
phi=[9.000000 -18.000000 9.000000 ]
phi1=[-10.009867 1.009867 2.663378 ] phi0=6.336622 gives y^{p+1}(t_n-theta*h) at theta=0.568023
M(infty)
| -0 | 0 | 0 |
| 3.28185 | 0.211361 | -0.00896962 |
| 28.6933 | 4.98052 | -0.211361 |
Method c=[1/3,2/3,1],gamma=0.42942878684529,beta=0.02644330273460, c=[
0.333333 , 0.666667, 1]
AUBV (scaled)
| 0.429429 | -0 | -0 |
| 3.74754 | 0.429429 | -0 |
| -0.136492 | -0.14157 | 0.429429 |
|
| 1 | -0.0960955 | -0.175175 |
| 1 | -3.5103 | -2.62649 |
| 1 | 0.848634 | 0.420898 |
|
| -0.136492 | -0.14157 | 0.429429 |
| 0 | 0 | 1 |
| -2.47161 | 0.340608 | 1.0968 |
|
| 1 | 0.848634 | 0.420898 |
| 0 | 0 | 0 |
| 0 | 1.03421 | 0 |
|
Maximum coefficient scaled is 3.747542 .
irks(0.429429,[0.333333,0.666667,1], [0.0264433],[ 1; ])
[alpha,beta,gamma,stageerror]
| -0.00343983 | -9.69347e-06 | 0.0199535 | -0.0200004 |
| 0 | -0 | -0 | -0.288969 |
| 0.0264433 | 0.10483 | -0.10553 | -0.00343983 |
Error estimation
phi=[9.000000 -18.000000 9.000000 ]
phi1=[-9.633571 0.633571 2.788810 ] phi0=6.211190 gives y^{p+1}(t_n-theta*h) at theta=0.563377
M(infty)
| 0 | 0 | 0 |
| 2.863 | 0.145985 | -0.00386032 |
| 30.0487 | 5.52067 | -0.145985 |
Method c=[1/2,1,1],beta=1/3, c=[
0.5 , 1, 1]
AUBV (scaled)
| 0.444444 | 0 | 0 |
| 0.984127 | 0.444444 | 0 |
| 0.514991 | -0.230453 | 0.444444 |
|
| 1 | 0.0555556 | -0.194444 |
| 1 | -0.428571 | -0.873016 |
| 1 | 0.271017 | 0.0570253 |
|
| 0.514991 | -0.230453 | 0.444444 |
| 0 | 0 | 1 |
| -0.666667 | 0.190476 | 0.642857 |
|
| 1 | 0.271017 | 0.0570253 |
| 0 | 0 | 0 |
| 0 | -0.166667 | 0 |
|
Maximum coefficient scaled is 0.984127 .
irks(0.444444,[0.5,1,1], [0.333333],[ 1; ])
[alpha,beta,gamma,stageerror]
| 0.0048011 | -0.00710366 | 0.0414544 | -0.0671296 |
| 0 | 0 | 0 | -0.324074 |
| 0.333333 | -0.0833333 | -0.0277778 | 0.0048011 |
Error estimation
phi=[0.000000 0.000000 0.000000 ]
phi1=[-8.000000 1.691345 2.308655 ] phi0=4.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| -0 | -0 | -0 |
| 1.77381 | 0.178571 | -0.0595238 |
| 6.32143 | 0.535714 | -0.178571 |
Method c=[1/2,1,1],beta=-1/20, c=[
0.5 , 1, 1]
AUBV (scaled)
| 0.444444 | 0 | 0 |
| 3.24336 | 0.444444 | 0 |
| -0.1659 | -0.103432 | 0.444444 |
|
| 1 | 0.0555556 | -0.194444 |
| 1 | -2.6878 | -3.13225 |
| 1 | 0.824888 | 0.483875 |
|
| -0.1659 | -0.103432 | 0.444444 |
| 0 | 0 | 1 |
| -2.2 | 0.332394 | 1.26761 |
|
| 1 | 0.824888 | 0.483875 |
| 0 | -0 | -0 |
| 0 | 0.6 | 0 |
|
Maximum coefficient scaled is 3.243356 .
irks(0.444444,[0.5,1,1], [-0.05],[ 1; ])
[alpha,beta,gamma,stageerror]
| 0.0048011 | 0.0144974 | 0.0198533 | -0.0298611 |
| -0 | 0 | -0 | -0.382669 |
| -0.05 | 0.108333 | -0.110833 | 0.0048011 |
Error estimation
phi=[0.000000 0.000000 0.000000 ]
phi1=[-8.000000 0.666099 3.333901 ] phi0=4.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
| 0 | -0 | -0 |
| 0.207688 | -0.282969 | -0.0141484 |
| 19.8463 | 5.65937 | 0.282969 |