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annotate +time/+rk/butcherTableau.m @ 1223:9fddc8749445 rv_diffOp_test

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Closing branch
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 05 Aug 2019 10:48:37 +0200
parents e0560bc4fb7d
children
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846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
1 function [s,a,b,c] = butcherTableau(order)
1011
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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2 % TODO: Change order from a double to string.
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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3 switch order
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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4
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
5 case 3
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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6 % TVD (Total Variational Diminishing)
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
7 s = 3;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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8 a = zeros(s,s-1);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
9 a(2,1) = 1;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
10 a(3,1) = 1/4; a(3,2) = 1/4;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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11 b = [1/6, 1/6, 2/3];
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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12 c = [0 1 1/2];
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
13 case 4
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
14 % Standard RK4
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
15 s = 4;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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16 a = zeros(s,s-1);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
17 a(2,1) = 1/2;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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18 a(3,1) = 0; a(3,2) = 1/2;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
19 a(4,1) = 0; a(4,2) = 0; a(4,3) = 1;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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20 b = [1/6 1/3 1/3 1/6];
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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21 c = [0, 1/2, 1/2, 1];
1011
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
diff changeset
22 % case 4-3/8
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
diff changeset
23 % % 3/8 RK4 (Kuttas method). Lower truncation error, more flops
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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24 % s = 4;
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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25 % a = zeros(s,s-1);
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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26 % a(2,1) = 1/3;
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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27 % a(3,1) = -1/3; a(3,2) = 1;
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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28 % a(4,1) = 1; a(4,2) = -1; a(4,3) = 1;
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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29 % b = [1/8 3/8 3/8 1/8];
e0560bc4fb7d Add todo:s for time stepping with RV
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 846
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30 % c = [0, 1/3, 2/3, 1];
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
31 case 6
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
32 % Runge-Kutta 6 from Alshina07
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
33 s = 7;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
34 a = zeros(s,s-1);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
35 a(2,1) = 4/7;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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36 a(3,1) = 115/112; a(3,2) = -5/16;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
37 a(4,1) = 589/630; a(4,2) = 5/18; a(4,3) = -16/45;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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38 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);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
39 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;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
40 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);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
41 b = [1/12 0 0 0 5/12 5/12 1/12];
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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42 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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43 otherwise
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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44 error('That Runge-Kutta order is not implemented', order)
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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45
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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46 end