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The pseudospectral method for third-order differential equations
Huang, Weizhang Sloan, David M.
Huang, Weizhang
Sloan, David M.
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Abstract
Generalized quadrature rules are derived which assist in the selection of collocation points for the pseudospectral solution of differential equations. In particular, it is shown that for an nth-order differential equation in one space dimension with two-point derivative boundary conditions, an ideal choice of interior collocation points is the set of zeros of a Jacobi polynomial. The pseudospectral solution of a third-order initial-boundary value problem is considered and accuracy is assessed by examining how well the discrete eigenproblem approximates the continuous one. Convergence is established for a special choice of collocation points and numerical results are included to demonstrate the viability of the approach.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/0729094.
Date
1992-12-01
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Society for Industrial and Applied Mathematics
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Keywords
pseudospect method, third-order differential equation, generalized quadrature rules, Jacobi polynomials
Citation
Huang, Weizhang & Sloan, David M. "The pseudospectral method for third-order differential equations." SIAM J. Numer. Anal., 29(6), 1626–1647. (22 pages). http://dx.doi.org/10.1137/0729094.