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annotate +time/+rk/rungekutta_4.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents c6fcee3fcf1b
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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