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Convert Rungekutta4SecondOrder to take F(t,v,v_t) instead of matrices
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 08 Jan 2019 12:34:29 +0100
parents 0344fff87139
children
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1 % Returns the coefficients used in a RK method as defined by a Butcher Tableau.
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2 %
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3 % @param method - string specifying which Runge-Kutta method to be used.
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4 % @return s - number of stages
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5 % @return a - coefficents for intermediate stages
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6 % @return b - weights for summing stages
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7 % @return c - time step coefficents for intermediate stages
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8 function [s,a,b,c] = butcherTableau(method)
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9 switch method
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10 case "tvd-3"
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11 % TVD (Total Variational Diminishing)
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12 s = 3;
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13 a = zeros(s,s-1);
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14 a(2,1) = 1;
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15 a(3,1) = 1/4; a(3,2) = 1/4;
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16 b = [1/6, 1/6, 2/3];
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17 c = [0 1 1/2];
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18 case "rk4"
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19 % Standard RK4
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20 s = 4;
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21 a = zeros(s,s-1);
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22 a(2,1) = 1/2;
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23 a(3,1) = 0; a(3,2) = 1/2;
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24 a(4,1) = 0; a(4,2) = 0; a(4,3) = 1;
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25 b = [1/6 1/3 1/3 1/6];
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26 c = [0, 1/2, 1/2, 1];
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27 case "rk4-3/8"
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28 % 3/8 RK4 (Kuttas method). Lower truncation error, more flops.
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29 % Irreducible, unlike standard rk4.
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30 s = 4;
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31 a = zeros(s,s-1);
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32 a(2,1) = 1/3;
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33 a(3,1) = -1/3; a(3,2) = 1;
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34 a(4,1) = 1; a(4,2) = -1; a(4,3) = 1;
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35 b = [1/8 3/8 3/8 1/8];
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36 c = [0, 1/3, 2/3, 1];
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37 case "rk6"
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38 % Runge-Kutta 6 from Alshina07
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39 s = 7;
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40 a = zeros(s,s-1);
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41 a(2,1) = 4/7;
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42 a(3,1) = 115/112; a(3,2) = -5/16;
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43 a(4,1) = 589/630; a(4,2) = 5/18; a(4,3) = -16/45;
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44 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);
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45 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;
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46 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);
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47 b = [1/12 0 0 0 5/12 5/12 1/12];
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48 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
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49 otherwise
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50 error('Runge-Kutta method %s is not implemented', method)
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51 end