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annotate +time/Rungekutta.m @ 983:b89379fb0814 feature/timesteppers

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Convert Rungekutta4 to take F(t,y) instead of a matrix
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 08 Jan 2019 12:07:57 +0100
parents 34b3d092a4d0
children 0585a2ee7ee7
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1 classdef Rungekutta < time.Timestepper
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2 properties
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3 F % RHS of the ODE
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4 dt % Time step
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5 t % Time point
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6 v % Solution vector
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7 n % Time level
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8 scheme % The scheme used for the time stepping, e.g rk4, rk6 etc.
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9 coeffs % Butcher tableau coefficients
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10 V % All stage approximations in most recent time step
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11 K % All stage rates in most recent time step
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12 end
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13
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14
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15 methods
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16 % Timesteps v_t = F(v,t), using the specified RK method from t = t0 with
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17 % timestep dt and initial conditions v = v0
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18 function obj = Rungekutta(F, dt, t0, v0, method, discreteData)
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19 default_arg('method',"rk4");
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20 default_arg('discreteData', []);
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21 obj.F = F;
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22 obj.dt = dt;
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23 obj.t = t0;
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24 obj.v = v0;
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25 obj.n = 0;
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26
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27 % Extract the coefficients for the specified method
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28 % used for the RK updates from the Butcher tableua.
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29 [s,a,b,c] = time.rk.butcherTableau(method);
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30 obj.coeffs = struct('s',s,'a',a,'b',b,'c',c);
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31
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32 if isempty(discreteData)
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33 % TODO: method "rk4" is also implemented in the butcher tableau, but the rungekutta_4.m implementation
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34 % might be slightly more efficient. Need to do some profiling before deciding whether or not to keep it.
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35 if (method == "rk4")
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36 obj.scheme = @(v,t,n) time.rk.rungekutta_4(v ,t, dt, F);
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37 else
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38 obj.scheme = @(v,t,n) time.rk.rungekutta(v, t, dt, F, obj.coeffs);
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39 end
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40 else
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41 obj.scheme = @(v,t,n) time.rk.rungekuttaDiscreteData(v, t, dt, F, obj.coeffs, discreteData, n);
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42 end
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43 end
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44
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45 % v: Current solution
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46 % t: Current time
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47 % V: All stage approximations in most recent time step
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48 % K: All stage rates in most recent time step
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49 % T: Time points (corresponding to V and K) in most recent time step
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50 function [v,t,V,T,K] = getV(obj)
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51 v = obj.v;
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52 t = obj.t;
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53 V = obj.V;
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54 K = obj.K;
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55 T = obj.t + obj.dt*obj.coeffs.b;
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56 end
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57
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58 function obj = step(obj)
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59 [obj.v, obj.V, obj.K] = obj.scheme(obj.v, obj.t, obj.n);
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60 obj.t = obj.t + obj.dt;
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61 obj.n = obj.n + 1;
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62 end
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63
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64 % Returns a vector of time points, including substage points,
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65 % in the time interval [t0, tEnd].
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66 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
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67 function tvec = timePoints(obj, t0, tEnd)
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68 N = round( (tEnd-t0)/obj.dt );
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69 tvec = zeros(N*obj.s, 1);
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70 s = obj.coeffs.s;
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71 c = obj.coeffs.c;
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72 for i = 1:N
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73 ind = (i-1)*s+1 : i*s;
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74 tvec(ind) = ((i-1) + c')*obj.dt;
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75 end
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76 end
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77
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78 % Returns a vector of quadrature weights corresponding to grid points
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79 % in time interval [t0, tEnd], substage points included.
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80 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
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81 function weights = quadWeights(obj, t0, tEnd)
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82 N = round( (tEnd-t0)/obj.dt );
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83 b = obj.coeffs.b;
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84 weights = repmat(b', N, 1);
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85 end
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86 end
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87 end