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annotate +time/Rungekutta4SecondOrder.m @ 1114:f2988a63c3aa feature/timesteppers

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Add tests for time.Rungekutta4 and time.Rungekutta4SecondOrder
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 10 Apr 2019 23:10:13 +0200
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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 dt
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5 t, n
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6 v, v_t
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7 end
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10 methods
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11 % Create a time stepper for
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12 % v_tt = F(t,v,v_t), v(t0) = v0, v_t(t0) = v0t
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13 % with step size dt, by rewriting on first order form
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14 function obj = Rungekutta4SecondOrder(F, dt, t0, v0, v0t)
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15 obj.F = F;
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16 obj.dt = dt;
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17 obj.t = t0;
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18 obj.n = 0;
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20 obj.v = v0;
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21 obj.v_t = v0t;
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22 end
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24 function [v,t] = getV(obj)
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25 v = obj.v;
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26 t = obj.t;
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27 end
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29 function [vt,t] = getVt(obj)
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30 vt = obj.v_t;
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31 t = obj.t;
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32 end
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34 function obj = step(obj)
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35 t = obj.t;
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36 v = obj.v;
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37 v_t = obj.v_t;
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38 dt = obj.dt;
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40 k1 = obj.F(t, v, v_t);
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41 k2 = obj.F(t + 1/2*dt, v + 1/2*dt*v_t, v_t + 1/2*dt*k1);
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42 k3 = obj.F(t + 1/2*dt, v + 1/2*dt*v_t + 1/4*dt^2*k1, v_t + 1/2*dt*k2);
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43 k4 = obj.F(t + dt, v + dt*v_t + 1/2*dt^2*k2, v_t + dt*k3);
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45 obj.v = v + dt*v_t + dt^2*(1/6)*(k1 + k2 + k3);
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46 obj.v_t = v_t + dt*(1/6)*(k1 + 2*k2 + 2*k3 + k4);
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47 obj.t = obj.t + obj.dt;
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48 obj.n = obj.n + 1;
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49 end
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50 end
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52 methods (Static)
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53 function k = getTimeStep(lambda)
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54 k = rk4.get_rk4_time_step(lambda);
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55 end
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56 end
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57 end