A Chebyshev Series Approximation for Linear Second- Order Partial Differential Equations with Complicated Conditions

Abstract

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 matrix

method, which has been given for solving of ordinary differential, integral and integro-differential equations. The

method is based on the approximation by the truncated bivariate Chebyshev series. PDEs and conditions are

transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the

unknown Chebyshev coefficients, via Chebyshev collocation points. Combining these matrix equations and then

solving the system yields the Chebyshev coefficients of the solution function. Finally, the effectiveness of the

method 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.

Keywords

• Partial differential equations; Chebyshev collocation method, Chebyshev polynomial solutions,