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annotate +time/Rungekutta.m @ 918:679f4ddd982f feature/timesteppers

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Add properties for stage approximations and stage rates in the Rungekutta class.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 26 Nov 2018 16:23:27 -0800
parents 8732d6bd9890
children 384ca2331a12
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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)
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19 default_arg('method',"rk4");
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20 obj.F = F;
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21 obj.dt = dt;
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22 obj.t = t0;
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23 obj.v = v0;
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24 obj.n = 0;
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25
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26 % Extract the coefficients for the specified method
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27 % used for the RK updates from the Butcher tableua.
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28 [s,a,b,c] = time.rk.butcherTableau(method);
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29 obj.coeffs = struct('s',s,'a',a,'b',b,'c',c);
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30
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31 % TODO: method "rk4" is also implemented in the butcher tableau, but the rungekutta_4.m implementation
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32 % might be slightly more efficient. Need to do some profiling before deciding whether or not to keep it.
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33 if (method == "rk4")
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34 obj.scheme = @time.rk.rungekutta_4;
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35 else
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36 obj.scheme = @(v,t,dt,F) time.rk.rungekutta(v, t , dt, F, obj.coeffs);
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37 end
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38 end
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39
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40 % v: Current solution
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41 % t: Current time
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42 % V: All stage approximations in most recent time step
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43 % K: All stage rates in most recent time step
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44 % T: Time points (corresponding to V and K) in most recent time step
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45 function [v,t,V,T,K] = getV(obj)
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46 v = obj.v;
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47 t = obj.t;
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48 V = obj.V;
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49 K = obj.K;
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50 T = obj.t + obj.dt*obj.coeffs.b;
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51 end
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52
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53 function obj = step(obj)
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54 [obj.v, obj.V, obj.K] = obj.scheme(obj.v, obj.t, obj.dt, obj.F);
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55 obj.t = obj.t + obj.dt;
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56 obj.n = obj.n + 1;
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57 end
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58 end
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59 end