Chebyshev polynomial solutions of second-order linear partial differential equations

The purpose of this study is to give a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients. For this purpose, Chebyshev matrix method is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and the unknown Chebyshev coefficients can be found approximately. Published by Elsevier Science Inc.