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Solution of Laplace's equation using interpolation functions

Ken Hill
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Laplace's equation can be solved numerically and very conveniently with Mathematica by the use of symbolic interpolation. Here we solve Laplace's equation in two dimensions for the case of two thin parallel wires on a square grid. Extension to triangular grids would be straight forward. The traditional approach for solving the equation of course is to use finite element methods. But finite element methods are laborious. Symbolic interpolation is attractive because of the compactness of the resulting code and the flexibility that Mathematica provides.

The general approach could find use for solving other boundary value problems, for example in elasticity.

*Applied Mathematics > Numerical Methods
*Engineering > Finite Element Methods
*Engineering > Mechanical and Structural Engineering

Laplace equation, interpolation function, symbolic interpolation
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FEMusingInterpolation.nb (737.8 KB) - Mathematica Notebook [for Mathematica 5.2]