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Mathematics of Computation

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Numerical solution of symmetric positive differential equations


Author: Theodore Katsanis
Journal: Math. Comp. 22 (1968), 763-783
MSC: Primary 65.65
DOI: https://doi.org/10.1090/S0025-5718-1968-0245214-9
MathSciNet review: 0245214
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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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DOI: https://doi.org/10.1090/S0025-5718-1968-0245214-9
Article copyright: © Copyright 1968 American Mathematical Society