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annotate +time/+rk/ButcherTableau.m @ 990:1066bb31bc95 feature/timesteppers

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Create class for butcher tableau
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 09 Jan 2019 09:09:15 +0100
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children 2f89959fb9f0
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1 classdef ButcherTableau
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2 properties
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3 a,b,c
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4 end
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5
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6 methods
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7 % A ButcherTableau describes a specific rungekutta method where
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8 % y(n+1) = y(n) + dt*b(i)*k(i)
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9 % k(i) = F(t + c(i)*dt, Y(i))
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10 % Y(i) = y(i) + dt*a(i,j)*k(j)
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11 % where repeating indecies imply summation
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12 function obj = ButcherTableau(a,b,c)
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13 s = length(c);
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14 assertSize(a, [s,s]);
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15 assertLength(b, s);
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16
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17 obj.a = a;
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18 obj.b = b;
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19 obj.c = c;
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20 end
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21
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22 function s = nStages(obj)
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23 s = length(obj.c);
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24 end
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25
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26 function b = isExplicit(obj)
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27 b = all(all(triu(obj.a)==0));
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28 end
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29
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30 % TBD: Add functions for checking accuracy, stability?
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31 end
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32
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33 methods(Static)
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34 % TVD (Total Variational Diminishing)
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35 function bt = tvd_3()
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36 a = [
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37 0, 0, 0;
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38 1, 0, 0;
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39 1/4, 1/4, 0;
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40 ];
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41 b = [1/6, 1/6, 2/3];
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42 c = [0 1 1/2];
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43
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44 bt = time.rk.ButcherTableau(a,b,c);
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45 end
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46
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47 % Standard RK4
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48 function bt = rk4()
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49 a = [
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50 0, 0, 0, 0;
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51 1/2, 0, 0, 0;
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52 0, 1/2, 0, 0;
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53 0, 0, 1, 0;
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54 ];
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55
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56 b = [1/6 1/3 1/3 1/6];
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57 c = [0, 1/2, 1/2, 1];
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58
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59 bt = time.rk.ButcherTableau(a,b,c);
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60 end
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61
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62 % 3/8 RK4 (Kuttas method). Lower truncation error, more flops.
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63 % Irreducible, unlike standard rk4.
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64 function bt = rk4_3_8()
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65 a = [
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66 0, 0, 0, 0;
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67 1/3, 0, 0, 0;
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68 -1/3, 1, 0, 0;
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69 1, -1, 1, 0;
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70 ];
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71
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72 b = [1/8 3/8 3/8 1/8];
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73 c = [0, 1/3, 2/3, 1];
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74
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75 bt = time.rk.ButcherTableau(a,b,c);
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76 end
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77
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78 % Runge-Kutta 6 from Alshina07
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79 function bt = rk6()
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80 a = zeros(7,7);
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81
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82 a(2,1) = 4/7;
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83
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84 a(3,1) = 115/112;
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85 a(3,2) = -5/16;
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86
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87 a(4,1) = 589/630;
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88 a(4,2) = 5/18;
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89 a(4,3) = -16/45;
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90
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91 a(5,1) = 229/1200 - 29/6000*sqrt(5);
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92 a(5,2) = 119/240 - 187/1200*sqrt(5);
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93 a(5,3) = -14/75 + 34/375*sqrt(5);
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94 a(5,4) = -3/100*sqrt(5);
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95
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96 a(6,1) = 71/2400 - 587/12000*sqrt(5);
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97 a(6,2) = 187/480 - 391/2400*sqrt(5);
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98 a(6,3) = -38/75 + 26/375*sqrt(5);
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99 a(6,4) = 27/80 - 3/400*sqrt(5);
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100 a(6,5) = (1+sqrt(5))/4
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101
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102 a(7,1) = -49/480 + 43/160*sqrt(5);
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103 a(7,2) = -425/96 + 51/32*sqrt(5);
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104 a(7,3) = 52/15 - 4/5*sqrt(5);
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105 a(7,4) = -27/16 + 3/16*sqrt(5);
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106 a(7,5) = 5/4 - 3/4*sqrt(5);
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107 a(7,6) = 5/2 - 1/2*sqrt(5);
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108
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109 b = [1/12 0 0 0 5/12 5/12 1/12];
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110 c = [0, 4/7, 5/7, 6/7, (5-sqrt(5))/10, (5+sqrt(5))/10, 1];
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111
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112 bt = time.rk.ButcherTableau(a,b,c);
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113 end
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114 end
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115 end