Numerical solution of symmetric positive differential equations

Katsanis, Theodore

doi:10.1090/S0025-5718-1968-0245214-9

Numerical solution of symmetric positive differential equations
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Math. Comp. 22 (1968), 763-783 Request permission

Abstract:

A finite-difference method for the solution of symmetric positive linear differential equations is developed. The method is applicable to any region with piecewise smooth boundaries. Methods for solution of the finite-difference equations are discussed. The finite-difference solutions are shown to converge at essentially the rate $O({h^{1/2}})$ as $h \to 0,h$, being the maximum distance between adjacent mesh-points. An alternate finite-difference method is given with the advantage that the finite-difference equations can be solved iteratively. However, there are strong limitations on the mesh arrangements which can be used with this method.

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Type-Insensitive Finite Difference Schemes

Numerical Techniques for the Solution of Symmetric Positive Linear Differential Equations

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