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comparison +time/+rk/ExplicitSecondOrder.m @ 1102:d4c895d4b524 feature/timesteppers

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Add skeleton for time.rk.ExplicitSecondOrder
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 09 Apr 2019 22:17:07 +0200
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1101:b895037bb701 1102:d4c895d4b524
1 classdef ExplicitSecondOrder < time.Timestepper
2 properties
3 F % RHS of the ODE
4 dt % Time step
5 t % Time point
6 v, vt % Solution state
7 n % Time level
8 bt
9 end
10
11
12 methods
13 % Timesteps v_tt = F(t,v,vt), using the specified ButcherTableau
14 % from t = t0 with timestep dt and initial conditions v(0) = v0
15 function obj = ExplicitSecondOrder(F, dt, t0, v0, v0t, bt)
16 assertType(bt, 'time.rk.ButcherTableau')
17 obj.F = F;
18 obj.dt = dt;
19 obj.t = t0;
20 obj.v = v0;
21 obj.vt = v0t;
22 obj.n = 0;
23
24 assert(bt.isExplicit())
25 obj.bt = bt;
26 end
27
28 function [v,t] = getV(obj)
29 v = obj.v;
30 t = obj.t;
31 end
32
33 function [vt,t] = getVt(obj)
34 vt = obj.vt;
35 t = obj.t;
36 end
37
38 function obj = step(obj)
39 s = obj.bt.nStages();
40 a = obj.bt.a;
41 b = obj.bt.b;
42 c = obj.bt.c;
43
44 t = obj.t;
45 v = obj.v;
46 vt = obj.vt;
47 dt = obj.dt;
48
49 k1 = obj.F(t, v, v_t);
50 k2 = obj.F(t + 1/2*dt, v + 1/2*dt*v_t, v_t + 1/2*dt*k1);
51 k3 = obj.F(t + 1/2*dt, v + 1/2*dt*v_t + 1/4*dt^2*k1, v_t + 1/2*dt*k2);
52 k4 = obj.F(t + dt, v + dt*v_t + 1/2*dt^2*k2, v_t + dt*k3);
53
54 % Compute rates K
55 K = zeros(length(v), s);
56 for i = 1:s
57 U_i = obj.v;
58 V_i = obj.vt;
59 for j = 1:i-1
60 U_i = U_i % + dt*a(i,j)*K(:,j);
61 V_i = V_i % + dt*a(i,j)*K(:,j);
62 end
63 K(:,i) = F(t+dt*c(i), U_i, V_i);
64 end
65
66 % Compute updated solution
67 v_next = v;
68 vt_next = vt;
69 for i = 1:s
70 v_next = v_next % + dt*b(i)*K(:,i);
71 vt_next = vt_next % + dt*b(i)*K(:,i);
72 end
73
74 obj.v = v_next;
75 obj.vt = vt_next;
76 obj.t = obj.t + obj.dt;
77 obj.n = obj.n + 1;
78 end
79
80
81 % Returns a vector of time points, including substage points,
82 % in the time interval [t0, tEnd].
83 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
84 function tvec = timePoints(obj, t0, tEnd)
85 % TBD: Should this be implemented here or somewhere else?
86 N = round( (tEnd-t0)/obj.dt );
87 tvec = zeros(N*obj.s, 1);
88 s = obj.coeffs.s;
89 c = obj.coeffs.c;
90 for i = 1:N
91 ind = (i-1)*s+1 : i*s;
92 tvec(ind) = ((i-1) + c')*obj.dt;
93 end
94 end
95
96 % Returns a vector of quadrature weights corresponding to grid points
97 % in time interval [t0, tEnd], substage points included.
98 % The time-step obj.dt is assumed to be aligned with [t0, tEnd] already.
99 function weights = quadWeights(obj, t0, tEnd)
100 % TBD: Should this be implemented here or somewhere else?
101 N = round( (tEnd-t0)/obj.dt );
102 b = obj.coeffs.b;
103 weights = repmat(b', N, 1);
104 end
105 end
106
107 methods(Static)
108 % TBD: Function name
109 function ts = methodFromStr(F, dt, t0, v0, methodStr)
110 try
111 bt = time.rk.ButcherTableau.(method);
112 catch
113 error('Runge-Kutta method ''%s'' is not implemented', methodStr)
114 end
115
116 ts = time.rk.Explicit(F, dt, t0, v0, bt);
117 end
118 end
119 end