Method bdf1, c=[ 0.5 , 1]

AUBV (scaled)

0.5	0
0.5	0.5

1	0
1	0

0.5	0.5
0	1

1	0
0	0

Maximum coefficient scaled is 0.500000 .

irks(0.5,[0.5,1],[])

[alpha,beta,gamma,stageerror]

-0.25	-0.145833	-0.1875	-0.125
0	0	0	-0.25

Error estimation

phi=[-2.000000 2.000000 ]
phi1=[0.376471 0.752941 ] phi0=-1.129412 gives y^{p+1}(t_n-theta*h) at theta=0.576471

M(infty)

0	0
0	0

Method bdf2, c=[ 0.333333 , 0.666667, 1]

AUBV (scaled)

0.222222	0	0
0.296296	0.222222	0
0.320988	0.296296	0.222222

1	0.111111	-0.037037
1	0.148148	-0.0493827
1	0.160494	-0.0534979

0.320988	0.296296	0.222222
0	0	1
-0.222222	-0.666667	1

1	0.160494	-0.0534979
0	0	0
0	-0.111111	0.037037

Maximum coefficient scaled is 1.000000 .

irks(0.222222,[0.333333,0.666667,1], [0.333333],[ 1; ])

[alpha,beta,gamma,stageerror]

-0.037037	-0.00925926	-0.0185185	-0.0123457
0	0	0	-0.0246914
0.333333	-0.101852	-0.037037	-0.037037

Error estimation

phi=[9.000000 -18.000000 9.000000 ]
phi1=[9.000000 -18.000000 9.000000 ] phi0=0.000000 gives y^{p+1}(t_n-theta*h) at theta=0.333333

M(infty)

0	0	0
0	0	-0
0	0	-0

Method bdf3, c=[ 0.25 , 0.5, 0.75, 1]

AUBV (scaled)

0.136364	0	0	0
0.22314	0.136364	0	0
0.253569	0.22314	0.136364	0
0.257155	0.253569	0.22314	0.136364

1	0.113636	-0.00568182	-0.00994318
1	0.140496	0.00206612	-0.0191116
1	0.136927	0.00802968	-0.0231381
1	0.129773	0.010416	-0.0240335

0.257155	0.253569	0.22314	0.136364
0	0	0	1
0.02131	-0.504884	-1.8843	2.18182
0.314733	-0.0721262	-1.98347	1.45455

1	0.129773	0.010416	-0.0240335
0	0	0	0
0	0.186053	-0.0429615	0.00896455
0	0.286319	-0.0191244	-0.0214466

Maximum coefficient scaled is 2.181818 .

irks(0.136364,[0.25,0.5,0.75,1], [0.0572917,0.375],[ 1 0; -0.190615 1; ])

[alpha,beta,gamma,stageerror]

-0.00390625	-0.00078125	-0.00195312	-0.000976562
0	-0	0	-0.00195312
0.0572917	-0.0195313	-0.00390625	-0.00292969
0.375	-0.078125	0	-0.00390625

Error estimation

phi=[-64.000000 192.000000 -192.000000 64.000000 ]
phi1=[-64.000000 192.000000 -192.000000 64.000000 ] phi0=0.000000 gives y^{p+1}(t_n-theta*h) at theta=0.375000

M(infty)

0	0	0	-0
0	0	0	0
0	0	-0	-0
0	0	-0	0

Method bdf4, c=[ 0.2 , 0.4, 0.6, 0.8, 1]

AUBV (scaled)

0.096	0	0	0	0
0.18432	0.096	0	0	0
0.215654	0.18432	0.096	0	0
0.210076	0.215654	0.18432	0.096	0
0.199248	0.210076	0.215654	0.18432	0.096

1	0.104	0.0016	-0.00352	-0.001472
1	0.11968	0.009472	-0.0041984	-0.00487424
1	0.104026	0.0110822	-0.00203213	-0.00743086
1	0.09395	0.00866222	-0.00010879	-0.00819043
1	0.0947022	0.00654312	0.000452812	-0.00796805

0.199248	0.210076	0.215654	0.18432	0.096
0	0	0	0	1
0.463004	0.584448	-0.7056	-3.68	3.5
1.0219	2.58624	0.672	-8.4	5
0.301862	1.80672	1.416	-5.2	2.5

1	0.0947022	0.00654312	0.000452812	-0.00796805
0	0	0	0	0
0	-0.161852	0.0819599	-0.00844754	-0.0181564
0	-0.880141	0.155848	0.0382167	-0.0721863
0	-0.824582	0.054679	0.0512709	-0.0460039

Maximum coefficient scaled is 8.400000 .

irks(0.096,[0.2,0.4,0.6,0.8,1], [0.00666667,0.07,0.4],[ 0.0241119 0.223352 1; 0.316382 1 0; 1 0 0; ])

[alpha,beta,gamma,stageerror]

-0.00032	-5.33333e-05	-0.00016	-6.4e-05
0	-0	-0	-0.000128
0.00666667	-0.00243556	-0.00032	-0.000192
0.07	-0.02	0	-0.000256
0.4	-0.0866667	0	-0.00032

Error estimation

phi=[625.000000 -2500.000000 3750.000000 -2500.000000 625.000000 ]
phi1=[625.000000 -2500.000000 3750.000000 -2500.000000 625.000000 ] phi0=0.000000 gives y^{p+1}(t_n-theta*h) at theta=0.400000

M(infty)

-0	-0	-0	0
-0	-0	0	-0
-0	-0	-0	-0
-0	-0	0	-0
-0	-0	0	-0

Method bdf5, c=[ 0.166667 , 0.333333, 0.5, 0.666667, 0.833333, 1]

AUBV (scaled)

0.0729927	0	0	0	0	0
0.159838	0.0729927	0	0	0	0
0.190172	0.159838	0.0729927	0	0	0
0.172984	0.190172	0.159838	0.0729927	0	0
0.155742	0.172984	0.190172	0.159838	0.0729927	0
0.158759	0.155742	0.172984	0.190172	0.159838	0.0729927

1	0.093674	0.00344688	-0.0014531	-0.000580112	-0.000153007
1	0.100503	0.00916997	-0.000613699	-0.00142802	-0.00100715
1	0.076997	0.00705786	0.00112844	-0.00119777	-0.00216045
1	0.0706797	0.00283998	0.00128809	-0.000275094	-0.0027601
1	0.0816042	0.00226359	0.000249165	0.000253335	-0.00269964
1	0.089512	0.00432316	-0.000418961	0.000139526	-0.00248358

0.158759	0.155742	0.172984	0.190172	0.159838	0.0729927
0	0	0	0	0	1
-0.702373	0.87532	1.97434	-0.655301	-6.07225	4.92701
-4.87037	1.21188	10.3149	4.4781	-22.1871	11.1679
-8.55528	-2.33625	14.0672	12.4521	-29.2887	11.8248
-4.25328	-2.64851	5.86933	7.83491	-13.2921	4.72993

1	0.089512	0.00432316	-0.000418961	0.000139526	-0.00248358
0	0	0	0	0	0
0	-0.34675	-0.183635	0.0292263	0.0209082	-0.0143319
0	-0.11528	-0.827407	0.0144343	0.133356	-0.0426296
0	1.83608	-1.09589	-0.117831	0.211566	-0.0183763
0	1.75976	-0.438741	-0.109107	0.0997667	0.00877029

Maximum coefficient scaled is 29.288721 .

irks(0.0729927,[0.166667,0.333333,0.5,0.666667,0.833333,1], [0.000587277,0.00868056,0.0787037,0.416667],[ 0.00228955 0.0356746 0.170779 1; 0.0523094 0.340012 1 0; 0.382128 1 0 0; 1 0 0 0; ])

[alpha,beta,gamma,stageerror]

-2.14335e-05	-3.06192e-06	-1.07167e-05	-3.57225e-06
-0	0	0	-7.14449e-06
0.000587277	-0.000225051	-2.14335e-05	-1.07167e-05
0.00868056	-0.00284851	-0	-1.4289e-05
0.0787037	-0.0231481	0	-1.78612e-05
0.416667	-0.0925926	-0	-2.14335e-05

Error estimation

phi=[-7776.000000 38880.000000 -77760.000000 77760.000000 -38880.000000 7776.000000 ]
phi1=[-7776.000000 38880.000000 -77760.000000 77760.000000 -38880.000000 7776.000000 ] phi0=0.000000 gives y^{p+1}(t_n-theta*h) at theta=0.416667

M(infty)

-0	0	0	-0
0	-0	-0	0
0	-0	-0	0
-0	-0	-0	-0
-0	-0	-0	0
-0	-0	-0	-0