Function Reference: Volume 3 (P-Z) - The MathWorks - #251

fixed mesh in xmesh. The cost depends strongly on the length of xmesh. When /71 > 0, it is not necessary to use a fine mesh near .■. = l.l to account for the coordinate singularity.

• The time integration is done with ode15s. pdepe exploits the capabilities of ode15s for solving the differential-algebraic equations that arise when Equation 2-2 contains elliptic equations, and for handling Jacobians with a specified sparsity pattern.

• After discretization, elliptic equations give rise to algebraic equations. If the elements of the initial conditions vector that correspond to elliptic equations are not "consistent" with the discretization, pdepe tries to adjust them before beginning the time integration. For this reason, the solution returned for the initial time may have a discretization error comparable to that at any other time. Ifthe mesh is sufficiently fine, pdepe can find consistent initial conditions close to the given ones. If pdepe displays a message that it has difficulty finding consistent initial conditions, try refining the mesh.

No adjustment is necessary for elements of the initial conditions vector that correspond to parabolic equations.

Examples Example 1. This example illustrates the straightforward formulation,

computation, and plotting of the solution of a single PDE.

dt òx\òx) This equation holds on an interval 0 < X < 1 for times t > 0. The PDE satisfies the initial condition

and boundary conditions