Method 2.2557, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | -0 | -0 | 0 | -0 | -0 |
-0.306308 | 0.2 | 0 | 0 | -0 | -0 |
0.29879 | 0.512572 | 0.2 | -0 | 0 | 0 |
-1.35469 | 0.85931 | 0.0251334 | 0.2 | -0 | 0 |
1.40868 | -2.25569 | -2.25569 | 1.95061 | 0.2 | 0 |
-1.38612 | 2.25571 | 1.58783 | -0.561094 | -0.259997 | 0.2 |
|
1 | -0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.506308 | 0.122523 | 0.00475691 | -0.0157982 | -0.0129095 |
1 | -0.411362 | -0.409574 | -0.281889 | -0.18398 | -0.11984 |
1 | 1.07025 | 0.144268 | -0.14905 | -0.198349 | -0.197361 |
1 | 1.95208 | 1.42693 | 0.00465678 | -1.31356 | -2.25571 |
1 | -0.836315 | -1.13776 | -0.373963 | 0.484123 | 1.14255 |
|
-1.38612 | 2.25571 | 1.58783 | -0.561094 | -0.259997 | 0.2 |
0 | 0 | 0 | 0 | 0 | 1 |
-0.861706 | 0.552272 | -1.7396 | -2.25571 | 1.231 | 1.80635 |
2.25572 | -0.670987 | -2.25566 | -2.25571 | 1.35284 | 1.42586 |
0.149383 | 1.35336 | -0.576711 | -2.25571 | 0.888421 | 0.710524 |
-2.0223 | 2.01799 | 0.44454 | -1.32929 | 0.317156 | 0.196912 |
|
1 | -0.836315 | -1.13776 | -0.373963 | 0.484123 | 1.14255 |
0 | 0 | 0 | 0 | 0 | 0 |
0 | 1.2674 | 0.524837 | -0.0639834 | -0.140473 | 0.496437 |
0 | 0.147937 | 0.393028 | -0.517639 | -0.44663 | 2.2557 |
0 | -0.269273 | -0.0391498 | -0.510571 | -0.629056 | 1.82425 |
0 | 0.374991 | -0.240194 | -0.196032 | -0.169863 | 0.621858 |
|
Maximum coefficient scaled is 2.255719 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0117422,0.0804784,0.217722,0.521666],[ -0.00992508 0.00639801 0.10847 1; 0.228451 -0.293726 1 0; -0.154226 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | 0.0155897 | -0.0157812 | -0.000499006 |
0 | -0 | -0 | 0.000573149 |
0.0117422 | -0.0142825 | 0.00815702 | -0.00848497 |
0.0804784 | -0.0209123 | -0.0093284 | -0.0040776 |
0.217722 | 0.0780127 | -0.111113 | -0.0172362 |
0.521666 | 0.442922 | -0.497335 | -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 -13306.267969 16431.267969 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
0 | -0 | -0 | 0 | 0 | 0 |
81.5978 | -3.58272 | -2.06738 | 0.288835 | 0.19361 | 0.0445627 |
542.77 | -26.9733 | -14.5409 | 1.94819 | 1.38304 | 0.341301 |
1459.52 | -76.6318 | -39.98 | 4.94355 | 3.80133 | 1.058 |
3557.51 | -196.897 | -94.8199 | 12.5027 | 8.85572 | 2.6011 |
6733.26 | -349.812 | -174.248 | 25.595 | 15.7838 | 4.3243 |
Method 2.2889, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | 0 | -0 | -0 | 0 | -0 |
0.0900472 | 0.2 | -0 | -0 | 0 | -0 |
0.370151 | -0.0919482 | 0.2 | -0 | 0 | -0 |
0.428269 | -0.577402 | 0.237574 | 0.2 | 0 | -0 |
2.28888 | -2.28888 | -2.28888 | 1.63161 | 0.2 | 0 |
-0.770586 | 1.38166 | 1.01482 | 0.324335 | -0.539304 | 0.2 |
|
1 | -0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.109953 | -0.0360189 | -0.0428057 | -0.0284815 | -0.0160804 |
1 | 0.121797 | 0.0454982 | -0.000282967 | -0.0315061 | -0.0430318 |
1 | 0.511559 | 0.325525 | 0.0971805 | -0.0711539 | -0.165387 |
1 | 1.45727 | 1.65163 | 0.563293 | -0.651237 | -1.58368 |
1 | -0.610927 | -0.855206 | -0.271543 | 0.487128 | 1.20399 |
|
-0.770586 | 1.38166 | 1.01482 | 0.324335 | -0.539304 | 0.2 |
-0 | -0 | -0 | 0 | 0 | 1 |
0.671199 | -1.65649 | -0.599097 | -2.28888 | 1.40459 | 1.52991 |
2.28888 | -0.404152 | -2.28888 | -2.28888 | 1.61503 | 1.16804 |
2.28888 | 0.923294 | -0.923164 | -2.28888 | 1.11116 | 0.5794 |
-0.804556 | 0.054732 | 2.28473 | -2.28888 | 0.534526 | 0.19058 |
|
1 | -0.610927 | -0.855206 | -0.271543 | 0.487128 | 1.20399 |
0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.938772 | 0.568839 | -0.0472526 | -0.130169 | 0.610005 |
0 | -0.0900424 | 0.250484 | -0.563255 | -0.436856 | 2.28888 |
0 | -1.69069 | -0.265299 | -0.397854 | -0.586599 | 1.69656 |
0 | 0.0288612 | -0.251653 | -0.177911 | -0.175079 | 0.581014 |
|
Maximum coefficient scaled is 2.288877 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0169673,0.0725054,0.184836,0.408038],[ -0.00936239 -0.0144257 0.138214 1; 0.144794 -0.513721 1 0; 0.236307 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | 0.0204106 | -0.020602 | -0.000574458 |
0 | -0 | 0 | -0.00110849 |
0.0169673 | -0.0230425 | 0.0161192 | -6.43351e-05 |
0.0725054 | -0.0044222 | -0.00819542 | 0.00253777 |
0.184836 | 0.158945 | -0.16186 | 0.00735756 |
0.408038 | 0.663118 | -0.644777 | -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 2191.434253 933.565747 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
2.72822e-10 | 0 | -0 | -0 | -0 | 0 |
264.36 | 21.7445 | -4.38356 | -0.706451 | 0.0847168 | 0.0448952 |
1121.11 | 91.2401 | -19.2279 | -3.08169 | 0.433013 | 0.238949 |
2818.82 | 227.497 | -49.1728 | -8.16427 | 1.15143 | 0.7445 |
6315.76 | 494.143 | -108.597 | -17.6036 | 2.37383 | 1.77476 |
15469.9 | 1248.03 | -257.425 | -40.9967 | 4.39374 | 3.27384 |
Method 2.3284, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | 0 | 0 | 0 | -0 | -0 |
2.27908 | 0.2 | -0 | 0 | 0 | 0 |
-1.33839 | -0.0120623 | 0.2 | -0 | -0 | -0 |
0.465679 | 0.0306009 | 0.0934446 | 0.2 | -0 | -0 |
1.48352 | -2.29801 | -2.29004 | 1.67536 | 0.2 | -0 |
-0.619597 | 1.16616 | 1.6287 | -0.148923 | -0.420583 | 0.2 |
|
1 | -0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | -2.07908 | -0.911632 | -0.30549 | -0.0985306 | -0.0335926 |
1 | 1.75046 | 0.665008 | 0.166397 | 0.00271657 | -0.0395889 |
1 | 0.0102756 | -0.0028858 | -0.0434901 | -0.103472 | -0.150114 |
1 | 2.22917 | 1.91248 | 0.581578 | -0.711721 | -1.66491 |
1 | -0.805756 | -0.960086 | -0.296721 | 0.501418 | 1.2082 |
|
-0.619597 | 1.16616 | 1.6287 | -0.148923 | -0.420583 | 0.2 |
-0 | 0 | 0 | 0 | 0 | 1 |
-0.574698 | 0.0189585 | -1.38349 | -2.31816 | 1.39158 | 1.62454 |
2.32843 | -0.519538 | -2.25681 | -2.32203 | 1.54921 | 1.2437 |
1.24366 | 0.669811 | -0.470757 | -2.31469 | 1.03181 | 0.609356 |
-1.80244 | 1.38786 | 1.06017 | -1.66665 | 0.415101 | 0.179487 |
|
1 | -0.805756 | -0.960086 | -0.296721 | 0.501418 | 1.2082 |
0 | -0 | -0 | -0 | -0 | -0 |
0 | 1.24127 | 0.551712 | -0.0434689 | -0.10803 | 0.565646 |
0 | -0.0229645 | 0.321853 | -0.513118 | -0.407755 | 2.30125 |
0 | -0.769201 | -0.0472464 | -0.441642 | -0.628736 | 1.74399 |
0 | 0.426469 | -0.184053 | -0.17866 | -0.178654 | 0.590142 |
|
Maximum coefficient scaled is 2.328430 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0162585,0.0815582,0.210659,0.478996],[ -0.0118356 -0.0013316 0.140772 1; 0.202638 -0.354619 1 0; -0.0039179 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | 0.0193396 | -0.0195311 | -0.000590345 |
-0 | 0 | -0 | -0.0125798 |
0.0162585 | -0.0224025 | 0.0146148 | 0.00747349 |
0.0815582 | -0.0183158 | -0.00449174 | -0.00236849 |
0.210659 | 0.0925777 | -0.111925 | 0.00738308 |
0.478996 | 0.526268 | -0.545046 | -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 -87008.647215 90133.647215 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
-1.31368e-10 | -0 | 0 | 0 | -0 | -0 |
180.571 | 5.33035 | -3.28815 | 0.0901227 | 0.220448 | 0.0569326 |
893.211 | 24.9368 | -16.9349 | 0.395306 | 1.17361 | 0.330311 |
2289 | 61.3491 | -44.1828 | 0.655614 | 3.08296 | 0.991188 |
5297.87 | 129.741 | -100.019 | 2.02708 | 6.80707 | 2.36039 |
10953.5 | 293.916 | -201.35 | 6.09681 | 12.9791 | 4.14183 |
Method 2.4673, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | -0 | 0 | 0 | -0 | -0 |
-0.0267078 | 0.2 | 0 | 0 | -0 | -0 |
-0.560162 | 0.243233 | 0.2 | 0 | -0 | -0 |
-0.278215 | 0.603649 | -0.34675 | 0.2 | -0 | -0 |
-0.959949 | 0.33036 | -0.45316 | 0.357285 | 0.2 | -0 |
2.46728 | 2.46728 | -2.1955 | -1.5802 | 1.2992 | 0.2 |
|
1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.226708 | 0.0106831 | -0.0287951 | -0.0247454 | -0.0151463 |
1 | 0.716929 | 0.149478 | -0.0495324 | -0.0875425 | -0.0784925 |
1 | 0.621316 | 0.364467 | 0.246124 | 0.153961 | 0.0677326 |
1 | 1.52546 | 0.691828 | 0.160047 | -0.194043 | -0.472678 |
1 | -1.65806 | 0.20378 | 0.427148 | -0.574226 | -2.17263 |
|
2.46728 | 2.46728 | -2.1955 | -1.5802 | 1.2992 | 0.2 |
-0 | -0 | 0 | -0 | -0 | 1 |
-0.694074 | -2.46728 | -2.46541 | 1.86202 | 1.16067 | 0.136793 |
2.46728 | -0.165705 | -2.46728 | -1.33346 | 2.46728 | -0.0455139 |
1.55101 | 2.46728 | -0.614918 | -2.46728 | 1.2949 | 0.236293 |
-0.00654125 | -0.36726 | 0.959899 | -0.278895 | -0.20021 | 0.23088 |
|
1 | -1.65806 | 0.20378 | 0.427148 | -0.574226 | -2.17263 |
0 | -0 | -0 | -0 | -0 | -0 |
0 | 2.46728 | 0.635786 | -0.537241 | -0.219318 | 1.61822 |
0 | -0.922594 | -0.603598 | -1.25691 | -0.860924 | 2.22238 |
0 | -2.46728 | -0.97106 | -0.562702 | -0.221745 | 2.46728 |
0 | -0.337874 | -0.470563 | -0.416154 | -0.286629 | 0.842873 |
|
Maximum coefficient scaled is 2.467278 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0341188,0.0118461,-0.0507943,0.00468845],[ -0.00512335 -0.00518154 0.624232 1; -0.225669 0.139097 1 0; 1 0 0 0; -0.700071 1 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | -0.0546936 | 0.0545022 | -0.0007043 |
-0 | -0 | 0 | 0.000165869 |
0.0341188 | -0.0448705 | 0.0447105 | 0.00255036 |
0.0118461 | -4.19642e-05 | 0.0341052 | 0.00637219 |
-0.0507943 | 1.09153 | -1.07945 | 0.011525 |
0.00468845 | 1.26053 | -1.31135 | -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 3128.369385 -3.369385 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
0 | 0 | -0 | -0 | -0 | 0 |
-9.62763 | -0.554489 | -10.2047 | -3.84579 | -0.665542 | -0.052419 |
-10.5916 | -2.22406 | -4.73783 | -1.54415 | -0.129322 | 0.0541793 |
-37.5352 | -9.88069 | 12.6749 | 5.47646 | 1.52443 | 0.457995 |
-42.5459 | -28.3974 | -9.70076 | -1.9591 | 0.747711 | 0.980782 |
-426.809 | -34.8862 | -293.846 | -112.182 | -20.2971 | -0.931845 |
Method 2.5263, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | -0 | -0 | -0 | 0 | 0 |
-0.227152 | 0.2 | 0 | -0 | 0 | 0 |
-0.346487 | 0.0274472 | 0.2 | -0 | 0 | 0 |
-0.129818 | 0.700561 | -0.602961 | 0.2 | 0 | 0 |
-0.399363 | 0.214746 | -0.607169 | 0.247374 | 0.2 | 0 |
2.52626 | 2.52626 | -2.52626 | -1.29018 | 1.14089 | 0.2 |
|
1 | -0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.427152 | 0.0908609 | -0.00474173 | -0.0183311 | -0.0135428 |
1 | 0.719039 | 0.236637 | 0.0284037 | -0.0391389 | -0.0525813 |
1 | 0.632218 | 0.535032 | 0.458507 | 0.345769 | 0.220165 |
1 | 1.34441 | 0.920752 | 0.525629 | 0.175776 | -0.13747 |
1 | -1.57697 | 0.382505 | 0.667073 | -0.266156 | -1.76873 |
|
2.52626 | 2.52626 | -2.52626 | -1.29018 | 1.14089 | 0.2 |
0 | 0 | 0 | 0 | 0 | 1 |
2.52626 | -2.23794 | -2.52626 | -0.458566 | 2.32318 | 0.0864927 |
2.52626 | -0.208959 | -1.08117 | -2.52626 | 2.52626 | 0.220322 |
1.36814 | 2.52626 | -0.464996 | -2.35653 | 1.10836 | 0.34503 |
-0.679987 | 0.0662801 | 1.01947 | -0.203799 | -0.309118 | 0.264881 |
|
1 | -1.57697 | 0.382505 | 0.667073 | -0.266156 | -1.76873 |
0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.286838 | 0.725724 | 0.150853 | -0.0247819 | 0.794049 |
0 | -1.45645 | -0.997077 | -1.42451 | -0.905757 | 2.14801 |
0 | -2.52626 | -1.14659 | -0.710204 | -0.276114 | 2.52626 |
0 | -0.157731 | -0.589846 | -0.527244 | -0.281707 | 0.9749 |
|
Maximum coefficient scaled is 2.526257 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.0303722,-0.00287553,-0.0105145,0.0605163],[ 0.0188608 -0.021384 0.636629 1; -0.205743 0.167175 1 0; 1 0 0 0; -0.0959464 1 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | -0.0377892 | 0.0375978 | -0.000598763 |
0 | 0 | -0 | 0.00137252 |
0.0303722 | -0.0362785 | 0.0344405 | 0.00350439 |
-0.00287553 | 0.024186 | 0.00636016 | 0.00801408 |
-0.0105145 | 1.02281 | -1.02505 | 0.0130073 |
0.0605163 | 1.43506 | -1.44924 | -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 5203.003213 -2078.003213 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
0 | -0 | -0 | -0 | -0 | -0 |
167.484 | -0.509202 | -15.8174 | -4.56395 | -0.658773 | -0.0381386 |
-24.5412 | -2.87431 | 0.0777832 | 0.205464 | 0.171024 | 0.0793334 |
-118.412 | -13.3316 | 2.65236 | 1.30315 | 0.737892 | 0.381583 |
313.64 | -37.8514 | -42.161 | -10.498 | -0.364069 | 0.940044 |
5495.5 | -40.6598 | -522.44 | -150.199 | -22.1257 | -0.507662 |
Method 2.5386, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | -0 | 0 | -0 | 0 | -0 |
-0.106974 | 0.2 | 0 | -0 | 0 | -0 |
-0.265067 | 0.0812306 | 0.2 | -0 | 0 | -0 |
-1.24683 | -0.405356 | 0.635969 | 0.2 | 0 | -0 |
-1.2713 | -0.734112 | 0.628871 | 0.176886 | 0.2 | -0 |
-2.27618 | -2.16366 | 2.50042 | 1.21525 | -1.01372 | 0.2 |
|
1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.306974 | 0.0427895 | -0.0191632 | -0.0221768 | -0.0145042 |
1 | 0.583837 | 0.161042 | -0.00718263 | -0.0555129 | -0.060117 |
1 | 1.61622 | 0.379855 | -0.214656 | -0.405808 | -0.432168 |
1 | 1.99965 | 0.658145 | -0.113873 | -0.476993 | -0.665635 |
1 | 2.53789 | 0.323937 | -0.280874 | 0.23242 | 1.25465 |
|
-2.27618 | -2.16366 | 2.50042 | 1.21525 | -1.01372 | 0.2 |
0 | 0 | -0 | -0 | 0 | 1 |
-0.0977076 | -2.53272 | -1.69317 | -0.840551 | 2.53815 | 0.0905125 |
0.943906 | -2.52422 | -2.5199 | -0.540338 | 2.53864 | -0.433186 |
-0.196921 | 1.88027 | -2.47414 | -1.91925 | 2.07612 | -0.149773 |
-1.34269 | -1.88305 | 0.756645 | 0.311532 | 0.33148 | -0.384103 |
|
1 | 2.53789 | 0.323937 | -0.280874 | 0.23242 | 1.25465 |
0 | -0 | -0 | -0 | -0 | -0 |
0 | 2.53549 | 1.18462 | -0.216081 | -0.678809 | 0.000267229 |
0 | 2.5351 | 1.31934 | -0.459053 | -0.522003 | 2.5278 |
0 | 0.783706 | 0.761645 | -0.300886 | -1.11213 | 0.663061 |
0 | 2.21019 | 0.742339 | -0.192461 | -0.556239 | 0.386564 |
|
Maximum coefficient scaled is 2.538638 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.0209101,-0.0152053,0.0407921,-0.122014],[ 0.0169161 0.010384 -0.0828715 1; 0.501694 -0.729494 1 0; -0.28458 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | 0.0148185 | -0.0150099 | 0.000451447 |
0 | -0 | 0 | -0.00043284 |
-0.0209101 | 0.0470925 | -0.0496439 | -0.00176975 |
-0.0152053 | 0.290882 | -0.313647 | -0.00423397 |
0.0407921 | 0.186547 | -0.196775 | -0.00782855 |
-0.122014 | 1.74691 | -1.721 | -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 4030.399351 -905.399351 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
0 | -0 | -0 | -0 | -0 | -0 |
28.3156 | -2.14306 | -3.04974 | -1.21149 | -0.362849 | -0.086037 |
32.1135 | 1.5382 | -2.62438 | -0.970336 | -0.137468 | 0.0150685 |
-26.5375 | 15.6315 | 4.6055 | 1.14095 | 0.840479 | 0.452892 |
400.859 | 25.1227 | -21.2248 | -9.52042 | -1.73075 | 0.379769 |
-1111.65 | 159.142 | 142.406 | 55.2331 | 17.353 | 5.35724 |
Method 2.602, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | 0 | -0 | -0 | -0 | 0 |
0.0753344 | 0.2 | 0 | -0 | -0 | 0 |
-2.21279 | 2.46379 | 0.2 | -0 | -0 | 0 |
-0.621304 | 1.05707 | 0.0131614 | 0.2 | -0 | 0 |
-2.60203 | 2.60203 | -0.205885 | 0.388535 | 0.2 | 0 |
2.60203 | 0.316599 | -0.584338 | -1.45949 | 1.08608 | 0.2 |
|
1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.124666 | -0.0301338 | -0.0410401 | -0.0280107 | -0.0159627 |
1 | 0.148996 | -0.965918 | -0.917085 | -0.603121 | -0.349503 |
1 | 0.151072 | -0.292928 | -0.319052 | -0.2621 | -0.220783 |
1 | 0.61735 | -0.815407 | -1.06036 | -1.00069 | -0.974549 |
1 | -1.16088 | 0.17014 | 0.110857 | -0.814729 | -2.12405 |
|
2.60203 | 0.316599 | -0.584338 | -1.45949 | 1.08608 | 0.2 |
0 | 0 | 0 | 0 | 0 | 1 |
-0.945852 | -2.60203 | -2.60203 | 2.57318 | 0.867162 | 0.107545 |
2.05993 | 0.761775 | -2.60203 | -1.52093 | 2.60203 | -0.173604 |
1.32642 | 2.49464 | -0.110754 | -2.60203 | 1.17071 | 0.323043 |
-0.9453 | 1.01027 | 0.382857 | -0.365331 | -0.152653 | 0.251668 |
|
1 | -1.16088 | 0.17014 | 0.110857 | -0.814729 | -2.12405 |
0 | -0 | -0 | -0 | -0 | -0 |
0 | 2.60203 | 0.515907 | -0.69195 | -0.224153 | 1.88334 |
0 | -1.12717 | -0.734321 | -1.16775 | -0.611623 | 2.54486 |
0 | -2.60203 | -1.21764 | -0.722347 | -0.231439 | 2.60203 |
0 | -0.181513 | -0.503027 | -0.38059 | -0.207032 | 0.883278 |
|
Maximum coefficient scaled is 2.602032 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [0.031688,0.0140203,-0.0858351,0.056722],[ -0.00573547 -0.000967753 0.660584 1; -0.225543 0.13735 1 0; 1 0 0 0; -0.968009 1 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | -0.0608223 | 0.0606309 | -0.00065503 |
-0 | -0 | 0 | -0.000492284 |
0.031688 | -0.036656 | 0.0348586 | -0.0157243 |
0.0140203 | 0.0419065 | -0.0110137 | -0.00483278 |
-0.0858351 | 1.04467 | -1.02578 | -0.0136992 |
0.056722 | 1.24258 | -1.33164 | -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 -30307.940399 33432.940399 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
-0 | 0 | 0 | 0 | 0 | 0 |
236.997 | -1.81507 | -13.9475 | -3.3816 | -0.420928 | -0.0133198 |
95.7936 | -3.2343 | -7.23676 | -1.64083 | -0.0728846 | 0.0672438 |
-690.32 | -8.29758 | 34.2663 | 8.8779 | 1.74562 | 0.44553 |
393.132 | -34.3541 | -32.1652 | -7.05484 | 0.0736228 | 0.92985 |
7314.86 | -73.5602 | -432.873 | -106.126 | -14.2741 | 0.1003 |
Method 3.1796, c=[
0.2 , 0.4, 0.6, 0.8, 1, 1]
AUBV (scaled)
0.2 | 0 | 0 | -0 | -0 | -0 |
0.0823709 | 0.2 | 0 | -0 | -0 | -0 |
-0.352435 | 0.667191 | 0.2 | -0 | 0 | 0 |
0.27998 | 3.17965 | 0.32002 | 0.2 | 0 | 0 |
-1.34462 | 0.122737 | 1.0666 | -0.126592 | 0.2 | 0 |
-3.17965 | -1.27572 | 3.17965 | -0.322169 | -0.397384 | 0.2 |
|
1 | 0 | -0.04 | -0.016 | -0.0048 | -0.00128 |
1 | 0.117629 | -0.0329484 | -0.0418845 | -0.0282359 | -0.016019 |
1 | 0.0852435 | -0.272779 | -0.27796 | -0.202723 | -0.134421 |
1 | -3.17965 | -2.71973 | -1.77745 | -1.09945 | -0.698528 |
1 | 1.08187 | -0.0377166 | -0.406432 | -0.450676 | -0.436851 |
1 | 2.79527 | 0.387098 | -0.229398 | 0.130457 | 0.775041 |
|
-3.17965 | -1.27572 | 3.17965 | -0.322169 | -0.397384 | 0.2 |
0 | -0 | 0 | 0 | 0 | 1 |
1.11723 | -3.17965 | -2.32002 | -0.135747 | 2.66185 | -0.223425 |
1.10751 | -3.17965 | -3.17965 | -0.124544 | 3.17965 | -0.982966 |
-2.67494 | 1.5017 | -3.17965 | 0.039869 | 1.9132 | -0.77983 |
-2.01285 | -1.89568 | 1.53385 | -0.276385 | 0.587661 | -0.515314 |
|
1 | 2.79527 | 0.387098 | -0.229398 | 0.130457 | 0.775041 |
0 | 0 | 0 | 0 | 0 | 0 |
0 | 2.07977 | 1.22121 | -0.156839 | -0.692933 | -0.0126601 |
0 | 3.17965 | 1.7222 | -0.523571 | -1.00589 | 1.73021 |
0 | 3.17965 | 1.35366 | -0.442467 | -1.16676 | 1.14108 |
0 | 2.57872 | 0.778587 | -0.191469 | -0.498889 | 0.469121 |
|
Maximum coefficient scaled is 3.179647 .
irks(0.2,[0.2,0.4,0.6,0.8,1,1], [-0.0176166,-0.0118489,0.034843,0.102662],[ 0.0027309 0.0350179 -0.272349 1; 0.293696 -0.302128 1 0; -0.211819 1 0 0; 1 0 0 0; ])
[alpha,beta,gamma,stageerror]
-0.000133778 | 0.0112134 | -0.0114049 | 0.000375421 |
-0 | 0 | -0 | 0.000306639 |
-0.0176166 | 0.0377675 | -0.0359589 | 0.00242153 |
-0.0118489 | 0.171998 | -0.188399 | 0.0246111 |
0.034843 | 0.323883 | -0.339309 | -0.000523313 |
0.102662 | 1.28938 | -1.26508 | -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 -803546.712748 806671.712748 ] phi0=-3125.000000 gives y^{p+1}(t_n-theta*h) at theta=0.500000
M(infty)
0 | 0 | 0 | 0 | -0 | -0 |
87.8154 | -3.07281 | -2.82298 | -0.620644 | -0.179921 | -0.0474856 |
75.3448 | 2.27844 | -2.38715 | -0.63008 | -0.0343624 | 0.0373348 |
-89.1472 | 24.7368 | 3.71017 | -0.0534279 | 0.583656 | 0.421682 |
-178.064 | 71.7389 | 12.3171 | 0.785895 | 1.51639 | 1.22668 |
-4748.7 | 243.749 | 157.278 | 31.9528 | 10.2012 | 3.99699 |