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• W2014082221 abstract "This paper concerns the numerical solution, in two or more dimensions, of boundary-value problems arising from linear partial differential equations, of which Laplace's and Poisson's equations furnish simple examples. Only techniques suitable for automatic computing machines are considered. The only method previously applicable to automatic machines is a straightforward iteration of an appropriate difference operator applied to an assumed trial solution on a network of points; as has been repeatedly pointed out, the rate of convergence of this iterative procedure is inordinately slow when the number of net points is large. The present paper shows how the employment of a Tschebyscheff polynomial of this same difference operator can cut the amount of work required in obtaining a solution by a very large factor—a factor of the order of magnitude of √N in the two-dimensional case, 3N in the three-dimensional case, where N is the number of net points. This method is an outgrowth of that developed by Flanders and Shortley [J. Appl. Phys. 21, 1326 (1950)] for employment of such Tschebyscheff-polynomial operators in the numerical solution of eigenvalue problems. The method is illustrated by a simple example involving Poisson's equation." @default.
• W2014082221 created "2016-06-24" @default.
• W2014082221 creator A5067788415 @default.
• W2014082221 date "1953-04-01" @default.
• W2014082221 modified "2023-09-25" @default.
• W2014082221 title "Use of Tschebyscheff‐Polynomial Operators in the Numerical Solution of Boundary‐Value Problems" @default.
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• W2014082221 doi "https://doi.org/10.1063/1.1721292" @default.
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