Matlab偏微分方程求解方法.doc

Matlab偏微分方程求解方法 目录： §1 Function Summary on 87 §2 Initial Value Problems on 88 §3 PDE Solver on 89 §4 Integrator Options on 92 §5 Examples” on 93 §1 Function Summary 1.1 PDE Solver” on 87 1,2 PDE Helper Function” on 87 1.3 PDE Solver This is the MATLAB PDE solver. PDE Initial-BoundaryValue Problem Solver Description pdepe Solve initial-boundary value problems for systems of parabolic and elliptic PDEs in one space variable and time. PDE Helper Function PDE Helper Function Description pdeval Evaluate the numerical solution of a PDE using the output of pdepe ? vInitial Value Problems pdepe solves systems of parabolic and elliptic PDEs in one spatial variable x and time t, of the form (10-2) The PDEs hold for .The interval [a, b] must be finite. m can be 0, 1, or 2, corresponding to slab, cylindrical, or spherical symmetry,respectively. If m 0, thena≥0 must also hold. In Equation 10-2, is a flux term and is a source term. The flux term must depend on . The coupling of the partial derivatives with respect to time is restricted to multiplication by a diagonal matrix. The diagonal elements of this matrix are either identically zero or positive. An element that is identically zero corresponds to an elliptic equation and otherwise to a parabolic equation. There must be at least one parabolic equation. An element of c that corresponds to a parabolic equation can vanish at isolated values of x if they are mesh points.Discontinuities in c and/or s due to material interfaces are permitted provided that a mesh point is placed at each interface. At the initial time t = t0, for all x the solution components satisfy initial conditions of the form (10-3) At the boundary x = a or x = b, for all t the solution components satisfy a boundary condition of the form (10-4) q(x, t) is a diagonal matrix with elements that are either identically zero or never zero. Note that the boundary conditions are expressed in terms of the f rather than partial de