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WIP: Make coefficients Rational for better generics #60

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WIP: Make coefficients Rational for better generics #60

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98 changes: 49 additions & 49 deletions src/ODE.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -270,13 +270,13 @@ end
# Bogacki–Shampine coefficients
const bs_coefficients = (3,
[ 0 0 0 0
1/2 0 0 0
0 3/4 0 0
2/9 1/3 4/9 0],
1//2 0 0 0
0 3//4 0 0
2//9 1//3 4//9 0],
# 2nd order b-coefficients
[7/24 1/4 1/3 1/8],
[7//24 1//4 1//3 1//8],
# 3rd order b-coefficients
[2/9 1/3 4/9 0],
[2//9 1//3 4//9 0],
)
ode23_bs(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, bs_coefficients...; kwargs...)

Expand All @@ -289,47 +289,47 @@ ode23_bs(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, bs_coefficients...; kwa
# Dormand-Prince coefficients
const dp_coefficients = (5,
[ 0 0 0 0 0 0
1/5 0 0 0 0 0
3/40 9/40 0 0 0 0
44/45 -56/15 32/9 0 0 0
19372/6561 -25360/2187 64448/6561 -212/729 0 0
9017/3168 -355/33 46732/5247 49/176 -5103/18656 0
35/384 0 500/1113 125/192 -2187/6784 11/84],
1//5 0 0 0 0 0
3//40 9//40 0 0 0 0
44//45 -56//15 32//9 0 0 0
19372//6561 -25360//2187 64448//6561 -212//729 0 0
9017//3168 -355//33 46732//5247 49//176 -5103//18656 0
35//384 0 500//1113 125//192 -2187//6784 11//84],
# 4th order b-coefficients
[5179/57600 0 7571/16695 393/640 -92097/339200 187/2100 1/40],
[5179//57600 0 7571//16695 393//640 -92097//339200 187//2100 1//40],
# 5th order b-coefficients
[35/384 0 500/1113 125/192 -2187/6784 11/84 0],
[35//384 0 500//1113 125//192 -2187//6784 11//84 0],
)
ode45_dp(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, dp_coefficients...; kwargs...)

# Fehlberg coefficients
const fb_coefficients = (5,
[ 0 0 0 0 0
1/4 0 0 0 0
3/32 9/32 0 0 0
1932/2197 -7200/2197 7296/2197 0 0
439/216 -8 3680/513 -845/4104 0
-8/27 2 -3544/2565 1859/4104 -11/40],
1//4 0 0 0 0
3//32 9//32 0 0 0
1932//2197 -7200//2197 7296//2197 0 0
439//216 -8 3680//513 -845//4104 0
-8//27 2 -3544//2565 1859//4104 -11//40],
# 4th order b-coefficients
[25/216 0 1408/2565 2197/4104 -1/5 0],
[25//216 0 1408//2565 2197//4104 -1//5 0],
# 5th order b-coefficients
[16/135 0 6656/12825 28561/56430 -9/50 2/55],
[16//135 0 6656//12825 28561//56430 -9//50 2//55],
)
ode45_fb(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, fb_coefficients...; kwargs...)

# Cash-Karp coefficients
# Numerical Recipes in Fortran 77
const ck_coefficients = (5,
[ 0 0 0 0 0
1/5 0 0 0 0
3/40 9/40 0 0 0
3/10 -9/10 6/5 0 0
-11/54 5/2 -70/27 35/27 0
1631/55296 175/512 575/13824 44275/110592 253/4096],
1//5 0 0 0 0
3//40 9//40 0 0 0
3//10 -9//10 6//5 0 0
-11//54 5//2 -70//27 35//27 0
1631//55296 175//512 575//13824 44275//110592 253//4096],
# 4th order b-coefficients
[37/378 0 250/621 125/594 0 512/1771],
[37//378 0 250//621 125//594 0 512//1771],
# 5th order b-coefficients
[2825/27648 0 18575/48384 13525/55296 277/14336 1/4],
[2825//27648 0 18575//48384 13525//55296 277//14336 1//4],
)
ode45_ck(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, ck_coefficients...; kwargs...)

Expand All @@ -339,22 +339,22 @@ ode45_ck(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, ck_coefficients...; kwa
# National Aeronautics and Space Administration.
const fb_coefficients_78 = (8,
[ 0 0 0 0 0 0 0 0 0 0 0 0
2/27 0 0 0 0 0 0 0 0 0 0 0
1/36 1/12 0 0 0 0 0 0 0 0 0 0
1/24 0 1/8 0 0 0 0 0 0 0 0 0
5/12 0 -25/16 25/16 0 0 0 0 0 0 0 0
1/20 0 0 1/4 1/5 0 0 0 0 0 0 0
-25/108 0 0 125/108 -65/27 125/54 0 0 0 0 0 0
31/300 0 0 0 61/225 -2/9 13/900 0 0 0 0 0
2 0 0 -53/6 704/45 -107/9 67/90 3 0 0 0 0
-91/108 0 0 23/108 -976/135 311/54 -19/60 17/6 -1/12 0 0 0
2383/4100 0 0 -341/164 4496/1025 -301/82 2133/4100 45/82 45/164 18/41 0 0
3/205 0 0 0 0 -6/41 -3/205 -3/41 3/41 6/41 0 0
-1777/4100 0 0 -341/164 4496/1025 -289/82 2193/4100 51/82 33/164 12/41 0 1],
2//27 0 0 0 0 0 0 0 0 0 0 0
1//36 1//12 0 0 0 0 0 0 0 0 0 0
1//24 0 1//8 0 0 0 0 0 0 0 0 0
5//12 0 -25//16 25//16 0 0 0 0 0 0 0 0
1//20 0 0 1//4 1//5 0 0 0 0 0 0 0
-25//108 0 0 125//108 -65//27 125//54 0 0 0 0 0 0
31//300 0 0 0 61//225 -2//9 13//900 0 0 0 0 0
2 0 0 -53//6 704//45 -107//9 67//90 3 0 0 0 0
-91//108 0 0 23//108 -976//135 311//54 -19//60 17//6 -1//12 0 0 0
2383//4100 0 0 -341//164 4496//1025 -301//82 2133//4100 45//82 45//164 18//41 0 0
3//205 0 0 0 0 -6//41 -3//205 -3//41 3//41 6//41 0 0
-1777//4100 0 0 -341//164 4496//1025 -289//82 2193//4100 51//82 33//164 12//41 0 1],
# 7th order b-coefficients
[41/840 0 0 0 0 34/105 9/35 9/35 9/280 9/280 41/840 0 0],
[41//840 0 0 0 0 34//105 9//35 9//35 9//280 9//280 41//840 0 0],
# 8th order b-coefficients
[0 0 0 0 0 34/105 9/35 9/35 9/280 9/280 0 41/840 41/840],
[0 0 0 0 0 34//105 9//35 9//35 9//280 9//280 0 41//840 41//840],
)
ode78_fb(F, x0, tspan; kwargs...) = oderkf(F, x0, tspan, fb_coefficients_78...; kwargs...)

Expand Down Expand Up @@ -603,23 +603,23 @@ ode4s_kr(F, x0, tspan; jacobian=nothing) = oderosenbrock(F, x0, tspan, kr4_coeff
const s4_coefficients = (0.5,
[ 0 0 0 0
2 0 0 0
48/25 6/25 0 0
48/25 6/25 0 0],
[19/9 1/2 25/108 125/108],
48//25 6//25 0 0
48//25 6//25 0 0],
[19//9 1//2 25//108 125//108],
[ 0 0 0 0
-8 0 0 0
372/25 12/5 0 0
-112/125 -54/125 -2/5 0],)
372//25 12//5 0 0
-112//125 -54//125 -2//5 0],)

ode4s_s(F, x0, tspan; jacobian=nothing) = oderosenbrock(F, x0, tspan, s4_coefficients...; jacobian=jacobian)

# Use Shampine coefficients by default (matching Numerical Recipes)
const ode4s = ode4s_s

const ms_coefficients4 = [ 1 0 0 0
-1/2 3/2 0 0
5/12 -4/3 23/12 0
-9/24 37/24 -59/24 55/24]
-1//2 3//2 0 0
5//12 -4//3 23//12 0
-9//24 37//24 -59//24 55//24]

# ODE_MS Fixed-step, fixed-order multi-step numerical method
# with Adams-Bashforth-Moulton coefficients
Expand Down