Mercurial > repos > public > sbplib

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

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
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:
rev   line source
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:
diff changeset
1 % Takes one time step of size dt using the rungekutta method
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:
diff changeset
2 % starting from v_0 and where the function F(v,t) gives the
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:
diff changeset
3 % time derivatives. coeffs is a struct holding the RK coefficients
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:
diff changeset
4 % for the specific method.
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:
diff changeset
5 function v = rungekutta(v, t , dt, F, coeffs)
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:
diff changeset
6 % Compute the intermediate stages k
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:
diff changeset
7 k = zeros(length(v), coeffs.s);
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:
diff changeset
8 for i = 1:coeffs.s
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:
diff changeset
9 u = v;
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:
diff changeset
10 for j = 1:i-1
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:
diff changeset
11 u = u + dt*coeffs.a(i,j)*k(:,j);
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:
diff changeset
12 end
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:
diff changeset
13 k(:,i) = F(u,t+coeffs.c(i)*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:
diff changeset
14 end
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:
diff changeset
15 % Compute the updated solution as a linear combination
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:
diff changeset
16 % of the intermediate stages.
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:
diff changeset
17 for i = 1:coeffs.s
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:
diff changeset
18 v = v + dt*coeffs.b(i)*k(:,i);
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:
diff changeset
19 end
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:
diff changeset
20 end