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annotate +time/+rk/rungekutta_4.m @ 1196:f6c571d8f22f feature/rv

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Add option to discretize Burgers1d using quasi-linear form
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 07 Aug 2019 13:28:21 +0200
parents c6fcee3fcf1b
children
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846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
1 % Takes one time step of size dt using the rungekutta method
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
2 % starting from v_0 and where the function F(v,t) gives the
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
3 % time derivatives.
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
4 function v = rungekutta_4(v, t , dt, F)
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
5 k1 = F(v ,t );
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
6 k2 = F(v+0.5*dt*k1,t+0.5*dt);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
7 k3 = F(v+0.5*dt*k2,t+0.5*dt);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
8 k4 = F(v+ dt*k3,t+ dt);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 0
diff changeset
9 v = v + (1/6)*(k1+2*(k2+k3)+k4)*dt;
0
48b6fb693025 Initial commit.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
10 end