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