Elliptic PDEs

Semianalytical and Numerical Method of Lines for Elliptic PDEs... 

Semianalytical Method for Elliptic PDEs in Rectangular Coordinates... 

The procedure involved in solving a linear steady state elliptic PDE is summarized as follows ... 

Transform the elliptic PDE from y coordinate to coordinate using the variable transformation = ye/h. 

Example 6.1 (heat transfer in a rectangle) is solved again using the numerical method of lines. The procedure involved in solving a linear or nonlinear steady state elliptic PDE numerically is summarized as follows ... 

Steady state linear elliptic PDEs in finite domains are solved by applying finite difference technique in both x and y coordinates in this section. When finite differences are applied, a linear elliptic PDE is converted to a system of linear algebraic equations. This resulting system of linear equations can be directly solved using Maple s solve or fsolve command. This is best illustrated with the following examples. 

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