Linear Elliptic PDE with Variable Coefficients

This function uses finite difference methods to solve a single linear elliptic PDE with variable coefficients on a rectangle.

This function uses finite difference methods to solve a fairly general, linear, elliptic partial differential equation on a rectangle. The equations that can be solved by this function are briefly described below, but more information can be found in any of the .mlx files in the download. The elliptic pde is

d/dx[a(x,y) dw/dx] +d/dy[b(x,y) dw/dy] +c(x,y) w = f(x,y)

The function can also handle fairly general boundary conditions, permitting Dirichlet, Neumann, or mixed conditions on any boundary. The boundary conditions are of the form

p(x)+q(x) w+r(x) [dw/dy]=0

for the horizontal boundaries and similar for the vertical.

Sparse matrices are used to maximize the allowable mesh density.

Several examples are provided in live scripts.