MATLAB Mathematics - SERC - Index of

5 Differential Equations
The output argument sol is a three-dimensional array, such that:
• sol(:,:,k) approximates component k of the solution u .
• sol(i,:,k) approximates component k of the solution at time tspan(i) and
mesh points xmesh(:).
• sol(i,j,k) approximates component k of the solution at time tspan(i) and
the mesh point xmesh(j).
Additional PDE Solver Arguments
For more advanced applications, you can also specify as input arguments solver
options and additional parameters that are passed to the PDE functions.
options
Structure of optional parameters that change the default
integration properties. This is the seventh input argument.
sol = pdepe(m,pdefun,icfun,bcfun,...
xmesh,tspan,options)
See “Changing PDE Integration Properties” on page 5-100 for
more information.
Solving PDE Problems
This section describes:
• The process for solving PDE problems using the MATLAB solver, pdepe
• Evaluating the solution at specific points
Example: A Single PDE
This example illustrates the straightforward formulation, solution, and
plotting of the solution of a single PDE
π 2 ∂u ------
∂t
=
∂ 2 u
---------
∂x 2
This equation holds on an interval 0 ≤ x ≤ 1 for times t ≥ 0 . At t = 0 , the
solution satisfies the initial condition
ux0 ( , ) = sinπx
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