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comparison +time/+rk/butcherTableau.m @ 888:8732d6bd9890 feature/timesteppers

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Add general Runge-Kutta class - Add a general Runge-Kutta class which time integrates the solution based on coefficients obtained from a Butcher tableau - Add butcher tableau which returns coefficents for the specified Runge-Kutta method - Remove RungKutta4proper, since obsolete
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 15 Nov 2018 17:10:01 -0800
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children d1c1615bd1a5
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887:50d5a3843099 888:8732d6bd9890
1 % Returns the coefficients used in a RK method as defined by a Butcher Tableau.
2 %
3 % @param method - string specifying which Runge-Kutta method to be used.
4 % @return s - number of stages
5 % @return a - coefficents for intermediate stages
6 % @return b - weights for summing stages
7 % @return c - time step coefficents for intermediate stages
8 function [s,a,b,c] = butcherTableau(method)
9 switch method
10 case "tvd-3"
11 % TVD (Total Variational Diminishing)
12 s = 3;
13 a = zeros(s,s-1);
14 a(2,1) = 1;
15 a(3,1) = 1/4; a(3,2) = 1/4;
16 b = [1/6, 1/6, 2/3];
17 c = [0 1 1/2];
18 case "rk4"
19 % Standard RK4
20 s = 4;
21 a = zeros(s,s-1);
22 a(2,1) = 1/2;
23 a(3,1) = 0; a(3,2) = 1/2;
24 a(4,1) = 0; a(4,2) = 0; a(4,3) = 1;
25 b = [1/6 1/3 1/3 1/6];
26 c = [0, 1/2, 1/2, 1];
27 case "rk4-3/8"
28 % 3/8 RK4 (Kuttas method). Lower truncation error, more flops
29 s = 4;
30 a = zeros(s,s-1);
31 a(2,1) = 1/3;
32 a(3,1) = -1/3; a(3,2) = 1;
33 a(4,1) = 1; a(4,2) = -1; a(4,3) = 1;
34 b = [1/8 3/8 3/8 1/8];
35 c = [0, 1/3, 2/3, 1];
36 case "rk6"
37 % Runge-Kutta 6 from Alshina07
38 s = 7;
39 a = zeros(s,s-1);
40 a(2,1) = 4/7;
41 a(3,1) = 115/112; a(3,2) = -5/16;
42 a(4,1) = 589/630; a(4,2) = 5/18; a(4,3) = -16/45;
43 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);
44 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;
45 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);
46 b = [1/12 0 0 0 5/12 5/12 1/12];
47 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
48 otherwise
49 error('That Runge-Kutta method is not implemented', method)
50 end