MATLAB Mathematics - SERC - Index of

Partial Differential Equations
ql = 0;
pr = pi * exp(-t);
qr = 1;
In the function pdex1bc, pl and ql correspond to the left boundary
conditions ( x = 0 ), and pr and qr correspond to the right boundary
condition ( x = 1 ).
5 Select mesh points for the solution. Before you use the MATLAB PDE
solver, you need to specify the mesh points ( t,
x)
at which you want pdepe
to evaluate the solution. Specify the points as vectors t and x.
The vectors t and x play different roles in the solver (see “MATLAB Partial
Differential Equation Solver” on page 5-91). In particular, the cost and the
accuracy of the solution depend strongly on the length of the vector x.
However, the computation is much less sensitive to the values in the vector
t.
This example requests the solution on the mesh produced by 20 equally
spaced points from the spatial interval [0,1] and five values of t from the
time interval [0,2].
x = linspace(0,1,20);
t = linspace(0,2,5);
6 Apply the PDE solver. The example calls pdepe with m = 0, the functions
pdex1pde, pdex1ic, and pdex1bc, and the mesh defined by x and t at which
pdepe is to evaluate the solution. The pdepe function returns the numerical
solution in a three-dimensional array sol, where sol(i,j,k) approximates
the kth component of the solution, u k , evaluated at t(i) and x(j).
m = 0;
sol = pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,x,t);
This example uses @ to pass pdex1pde, pdex1ic, and pdex1bc as function
handles to pdepe.
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