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comparison +time/+rk/rungekutta.m @ 917:878652b22157 feature/timesteppers

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Make time.rk.rungekutta return stage approximations and stage rates in addition to the solution after one time step.
author Martin Almquist <malmquist@stanford.edu>
date Mon, 26 Nov 2018 16:12:27 -0800
parents 8732d6bd9890
children
comparison
equal deleted inserted replaced
916:d1c1615bd1a5 917:878652b22157
1 % Takes one time step of size dt using the rungekutta method 1 % Takes one time step of size dt using the rungekutta method
2 % starting from @arg v and where the function F(v,t) gives the 2 % starting from @arg v and where the function F(v,t) gives the
3 % time derivatives. coeffs is a struct holding the RK coefficients 3 % time derivatives. coeffs is a struct holding the RK coefficients
4 % for the specific method. 4 % for the specific method.
5 function v = rungekutta(v, t , dt, F, coeffs) 5 % Also returns the stage approximations (V) and stage rates (K).
6 function [v, V, K] = rungekutta(v, t , dt, F, coeffs)
6 % Compute the intermediate stages k 7 % Compute the intermediate stages k
7 k = zeros(length(v), coeffs.s); 8 K = zeros(length(v), coeffs.s);
9 V = zeros(length(v), coeffs.s);
8 for i = 1:coeffs.s 10 for i = 1:coeffs.s
9 u = v; 11 u = v;
10 for j = 1:i-1 12 for j = 1:i-1
11 u = u + dt*coeffs.a(i,j)*k(:,j); 13 u = u + dt*coeffs.a(i,j)*K(:,j);
12 end 14 end
13 k(:,i) = F(u,t+coeffs.c(i)*dt); 15 V(:,i) = u;
16 K(:,i) = F(u,t+coeffs.c(i)*dt);
14 end 17 end
15 % Compute the updated solution as a linear combination 18 % Compute the updated solution as a linear combination
16 % of the intermediate stages. 19 % of the intermediate stages.
17 for i = 1:coeffs.s 20 for i = 1:coeffs.s
18 v = v + dt*coeffs.b(i)*k(:,i); 21 v = v + dt*coeffs.b(i)*k(:,i);