`pdeval`

Evaluates a pdepe solution and its derivative at chosen points.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

[uout, duoutdx] = pdeval(m, xmesh, ue, xout)

Interpolates the solution ue (one time slice) at the points xout.

Description

pdepe returns values only at the mesh points. pdeval interpolates with the same discretization the solver uses, so the derivative it returns is consistent with the flux used in the equation.

To see the solution over time, call it once for each row of sol.

Input arguments

m: Symmetry, as given to pdepe.
xmesh: The mesh used with pdepe.
ue: Row of the solution at a fixed time, for example sol(end, :, 1).
xout: Points at which to evaluate, inside the mesh range.

Output arguments

uout: Interpolated solution values.
duoutdx: Interpolated spatial derivative.

Example

Value between mesh points

m = 0;
x = linspace(0, 1, 11);
t = linspace(0, 0.1, 5);
sol = pdepe(m, @(x, t, u, dudx) deal(1, dudx, 0), @(x) sin(pi*x), @(xl, ul, xr, ur, t) deal(ul, 0, ur, 0), x, t);
u = pdeval(m, x, sol(end, :, 1), 0.55);
fprintf('%.3f\n', u)

Output

0.366

pdeval