A Chebyshev Series Approximation for Linear Second- Order Partial Differential Equations with Complicated Conditions
The purpose of this study is to present a new collocation method for the solution of second-order, linear partial differential equations (PDEs) under the most general conditions. The method has improved from Chebyshev matrixmethod, which has been given for solving of ordinary differential, integral and integro-differential equations. Themethod is based on the approximation by the truncated bivariate Chebyshev series. PDEs and conditions aretransformed into the matrix equations, which corresponds to a system of linear algebraic equations with theunknown Chebyshev coefficients, via Chebyshev collocation points. Combining these matrix equations and thensolving the system yields the Chebyshev coefficients of the solution function. Finally, the effectiveness of themethod is illustrated in several numerical experiments and error analysis is performed.Key words: Partial differential equations; Chebyshev collocation method, Chebyshev polynomial solutions,Bivariate Chebyshev series.
Partial differential equations; Chebyshev collocation method, Chebyshev polynomial solutions,