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annotate +time/Rungekutta4SecondOrder.m @ 1014:e547794a9407 feature/advectionRV

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Add boot-strapping to RungeKuttaExteriorRV - Higher order BDF approximations are successively used as increasing number of time levels are obtained.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 06 Dec 2018 11:30:47 +0100
parents c6fcee3fcf1b
children
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1 classdef Rungekutta4SecondOrder < time.Timestepper
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2 properties
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3 F
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4 k
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5 t
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6 w
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7 m
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8 D
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9 E
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10 S
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11 M
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12 C
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13 n
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14 end
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15
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16
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17 methods
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18 % Solves u_tt = Du + Eu_t + S by
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19 % Rewriting on first order form:
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20 % w_t = M*w + C(t)
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21 % where
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22 % M = [
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23 % 0, I;
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24 % D, E;
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25 % ]
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26 % and
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27 % C(t) = [
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28 % 0;
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29 % S(t)
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30 % ]
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31 % D, E, S can either all be constants or all be function handles,
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32 % They can also be omitted by setting them equal to the empty matrix.
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33 function obj = Rungekutta4SecondOrder(D, E, S, k, t0, v0, v0t)
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34 obj.D = D;
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35 obj.E = E;
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36 obj.S = S;
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37 obj.m = length(v0);
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38 obj.n = 0;
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39
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40
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41 if isa(D, 'function_handle') || isa(E, 'function_handle') || isa(S, 'function_handle')
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42 default_arg('D', @(t)sparse(obj.m, obj.m));
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43 default_arg('E', @(t)sparse(obj.m, obj.m));
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44 default_arg('S', @(t)sparse(obj.m, 1) );
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45
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46 if ~isa(D, 'function_handle')
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47 D = @(t)D;
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48 end
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49 if ~isa(E, 'function_handle')
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50 E = @(t)E;
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51 end
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52 if ~isa(S, 'function_handle')
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53 S = @(t)S;
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54 end
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55
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56 obj.k = k;
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57 obj.t = t0;
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58 obj.w = [v0; v0t];
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59
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60 % Avoid matrix formulation because it is VERY slow
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61 obj.F = @(w,t)[
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62 w(obj.m+1:end);
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63 D(t)*w(1:obj.m) + E(t)*w(obj.m+1:end) + S(t);
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64 ];
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65 else
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67 default_arg('D', sparse(obj.m, obj.m));
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68 default_arg('E', sparse(obj.m, obj.m));
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69 default_arg('S', sparse(obj.m, 1) );
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71 I = speye(obj.m);
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72 O = sparse(obj.m,obj.m);
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74 obj.M = [
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75 O, I;
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76 D, E;
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77 ];
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78 obj.C = [
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79 zeros(obj.m,1);
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80 S;
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81 ];
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82
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83 obj.k = k;
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84 obj.t = t0;
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85 obj.w = [v0; v0t];
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87 obj.F = @(w,t)(obj.M*w + obj.C);
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88 end
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89 end
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90
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91 function [v,t] = getV(obj)
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92 v = obj.w(1:end/2);
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93 t = obj.t;
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94 end
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95
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96 function [vt,t] = getVt(obj)
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97 vt = obj.w(end/2+1:end);
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98 t = obj.t;
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99 end
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100
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101 function obj = step(obj)
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c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
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102 obj.w = time.rk.rungekutta_4(obj.w, obj.t, obj.k, obj.F);
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103 obj.t = obj.t + obj.k;
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104 obj.n = obj.n + 1;
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105 end
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106 end
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107
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108
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109 methods (Static)
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110 function k = getTimeStep(lambda)
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111 k = rk4.get_rk4_time_step(lambda);
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112 end
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113 end
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114
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115 end