# 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 -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 0 0 -0 -0 -0 0 0 0 -0 -0 -0 -0