Mercurial > repos > public > sbplib
diff +time/+rk/butcherTableau.m @ 846:c6fcee3fcf1b feature/burgers1d
Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Thu, 20 Sep 2018 17:51:19 +0200 |
| parents | |
| children | e0560bc4fb7d |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+time/+rk/butcherTableau.m Thu Sep 20 17:51:19 2018 +0200 @@ -0,0 +1,37 @@ +function [s,a,b,c] = butcherTableau(order) + +switch order + + case 3 + % TVD (Total Variational Diminishing) + s = 3; + a = zeros(s,s-1); + a(2,1) = 1; + a(3,1) = 1/4; a(3,2) = 1/4; + b = [1/6, 1/6, 2/3]; + c = [0 1 1/2]; + case 4 + % Standard RK4 + s = 4; + a = zeros(s,s-1); + a(2,1) = 1/2; + a(3,1) = 0; a(3,2) = 1/2; + a(4,1) = 0; a(4,2) = 0; a(4,3) = 1; + b = [1/6 1/3 1/3 1/6]; + c = [0, 1/2, 1/2, 1]; + case 6 + % Runge-Kutta 6 from Alshina07 + s = 7; + a = zeros(s,s-1); + a(2,1) = 4/7; + a(3,1) = 115/112; a(3,2) = -5/16; + a(4,1) = 589/630; a(4,2) = 5/18; a(4,3) = -16/45; + a(5,1) = 229/1200 - 29/6000*sqrt(5); a(5,2) = 119/240 - 187/1200*sqrt(5); a(5,3) = -14/75 + 34/375*sqrt(5); a(5,4) = -3/100*sqrt(5); + a(6,1) = 71/2400 - 587/12000*sqrt(5); a(6,2) = 187/480 - 391/2400*sqrt(5); a(6,3) = -38/75 + 26/375*sqrt(5); a(6,4) = 27/80 - 3/400*sqrt(5); a(6,5) = (1+sqrt(5))/4; + a(7,1) = -49/480 + 43/160*sqrt(5); a(7,2) = -425/96 + 51/32*sqrt(5); a(7,3) = 52/15 - 4/5*sqrt(5); a(7,4) = -27/16 + 3/16*sqrt(5); a(7,5) = 5/4 - 3/4*sqrt(5); a(7,6) = 5/2 - 1/2*sqrt(5); + b = [1/12 0 0 0 5/12 5/12 1/12]; + c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1]; + otherwise + error('That Runge-Kutta order is not implemented', order) + +end \ No newline at end of file