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Error analysis of the Chebyshev collocation method for linear second-order partial differential equations. (English) Zbl 1325.65141

Summary: The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which is obtained by polynomial interpolation. The residual correction procedure is modified to the problem so that the absolute error may be estimated. Finally, the effectiveness of the method is illustrated in several numerical experiments such as Laplace and Poisson equations. Numerical results are overlapped with the theoretical results.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35G05 Linear higher-order PDEs
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