Method Order1, c=[ 0.3 , 1]

AUBV (scaled)

0.3 0
0.7 0.3
1 0
1 -0
0.7 0.3
0 1
1 -0
0 0

Maximum coefficient scaled is 0.700000 .

irks(0.3,[0.3,1],[])

[alpha,beta,gamma,stageerror]

-0.01 -0.0148333 -0.0345 -0.045
0 0 0 -0.01

Error estimation

phi=[-1.428571 1.428571 ]
phi1=[-0.238095 1.071429 ] phi0=-0.833333 gives y^{p+1}(t_n-theta*h) at theta=0.475000

M(infty)

-0 0
4.44444 0

Method Order2, c=[ 0.333333 , 0.666667, 1]

AUBV (scaled)

0.444444 0 -0
4.59259 0.444444 0
-0.493827 -0.148148 0.444444
1 -0.111111 -0.185185
1 -4.37037 -3.20988
1 1.19753 0.63786
-0.493827 -0.148148 0.444444
0 0 1
-2.625 0.375 1.125
1 1.19753 0.63786
0 -0 -0
0 1.125 0

Maximum coefficient scaled is 4.592593 .

irks(0.444444,[0.333333,0.666667,1], [-6.93889e-16],[ 1; ])

[alpha,beta,gamma,stageerror]

0.0048011 0.0163466 0.0180041 -0.0185185
-0 0 0 -0.304527
-0 0.12037 -0.12037 0.0048011

Error estimation

phi=[9.000000 -18.000000 9.000000 ]
phi1=[-9.629571 0.629571 2.790143 ] phi0=6.209857 gives y^{p+1}(t_n-theta*h) at theta=0.563328

M(infty)

0 -0 -0
2.25 0 0
32.625 6.375 0

Method Order3, c=[ 0.25 , 0.5, 0.75, 1]

AUBV (scaled)

0.225 0 -0 0
3.04901 0.225 0 0
-1.47877 -0.246497 0.225 -0
-1.48702 -0.23625 0.176625 0.225
1 0.025 -0.05 -0.0265625
1 -2.77401 -1.49951 -0.61544
1 2.25027 1.21088 0.50433
1 2.32165 1.26482 0.48295
-1.48702 -0.23625 0.176625 0.225
0 0 0 1
-2.5 0.422222 -1.74444 2.22222
5.49794 -1.58025 -5.16872 3.29218
1 2.32165 1.26482 0.48295
0 -0 -0 -0
0 1.6 0 -0.570833
0 -2.04115 0 0

Maximum coefficient scaled is 5.497942 .

irks(0.225,[0.25,0.5,0.75,1], [-1.46667e-15,-1.27744e-15],[ 1 0; 0 1; ])

[alpha,beta,gamma,stageerror]

0.000542057 0.00979947 -0.00807164 -0.000423177
-0 0 0 -0.0100235
-0 0.00608818 -0.00608818 0.00634961
-0 0.105131 -0.105131 0.000542057

Error estimation

phi=[-64.000000 192.000000 -192.000000 64.000000 ]
phi1=[83.980312 -29.970467 -44.019688 27.004922 ] phi0=-36.995078 gives y^{p+1}(t_n-theta*h) at theta=0.519512

M(infty)

-0 -0 -0 -0
3.2 -0 -0.190278 -0
-12.2469 -0 -0 -0
-1463.84 -284.313 -18.6667 0

Method Order3b, c=[ 0.25 , 0.5, 0.75, 1]

AUBV (scaled)

0.225 0 -0 0
1.54648 0.225 -0 0
1.06611 -0.165548 0.225 0
0.396781 -0.322453 0.238678 0.225
1 0.025 -0.05 -0.0265625
1 -1.27148 -0.748242 -0.333716
1 -0.375558 -0.142505 -0.0335467
1 0.461995 0.316046 0.089675
0.396781 -0.322453 0.238678 0.225
0 0 0 1
-2.71754 1.45029 -2.35731 2.22222
-1.42018 0.796935 -1.42018 1.02171
1 0.461995 0.316046 0.089675
0 0 0 0
0 1.40234 0 -0.266886
0 1.02171 0 0

Maximum coefficient scaled is 2.717544 .

irks(0.225,[0.25,0.5,0.75,1], [1.66533e-16,0.5],[ 1 0; 0 1; ])

[alpha,beta,gamma,stageerror]

0.000542057 0.00229181 -0.000563987 -0.00263672
0 -0 0 -0.0339203
0 0.050682 -0.050682 -0.00475968
0.5 -0.154155 -0.0958453 0.000542057

Error estimation

phi=[-64.000000 192.000000 -192.000000 64.000000 ]
phi1=[60.465493 5.301761 -67.534507 32.883627 ] phi0=-31.116373 gives y^{p+1}(t_n-theta*h) at theta=0.496548

M(infty)

-0 -0 -0 0
2.80468 -0 -0.088962 0.044481
-56.5435 -10.5883 -0.521106 0.260553
-125.348 -21.1766 -1.04221 0.521106

Method Order4, c=[ -0.63 , 0.67, 0.96, -0.82, 1]

AUBV (scaled)

0.285714 0 0 -0 -0
0.243064 0.285714 0 -0 -0
1.1208 -0.636817 0.285714 0 0
1.05141 -2.28847 0.675738 0.285714 -0
-0.334994 1.75515 -0.396767 -0.0918031 0.285714
1 -0.915714 0.7569 -0.590247 0.443298
1 0.141222 0.372303 -0.373424 0.100891
1 0.190299 2.63858 -0.382146 1.72536
1 -0.544394 4.23488 -1.16602 2.49562
1 -0.217305 -1.73419 -0.539766 -1.38779
-0.334994 1.75515 -0.396767 -0.0918031 0.285714
0 -0 -0 0 1
-1.10603 -3.79408 1.10032 0.562294 1.75
-4.14086 -4.19534 1.01591 1.31202 2.04167
-3.0498 -2.41926 -0.702988 1.72202 1.78646
1 -0.217305 -1.73419 -0.539766 -1.38779
0 0 0 0 0
0 1.48749 -0 0 -0.195632
0 3.9666 -3.47788 0 -3.9627
0 2.66357 -0 -0 -0

Maximum coefficient scaled is 4.234883 .

irks(0.285714,[-0.63,0.67,0.96,-0.82,1], [6.37923e-16,-1.68007e-14,1.55313e-14],[ -4.05022e-07 1 0; 1 0 0; -2.09993e-10 -0.000518424 1; ])

[alpha,beta,gamma,stageerror]

-0.000338649 0.00649603 -0.00759902 -0.00270238
0 -0 0 -0.00286924
0 0.00137435 -0.00137435 -0.00532625
-0 -0.345268 0.345268 -0.0200724
0 0.389824 -0.389824 -0.000338649

Error estimation

phi=[-37.491219 129.470160 -731.031559 26.168569 612.884048 ]
phi1=[-83.076793 -18.554238 -147.716329 50.614386 143.404433 ] phi0=55.328542 gives y^{p+1}(t_n-theta*h) at theta=0.917203

M(infty)

0 0 0 0 0
2.97498 -0 0 -0.0163027 0
23.7996 -10.4336 0 -0.990675 0
63.9257 -0 -0 -0 -0
-410.27 881.66 -65.8794 77.7904 -0