Polynomial solutions of certain differential equations

Abstract

In this paper, the Chebyshev matrix method is applied generalisations of the Hermite, Laguerre, Legendre and Chebyshev differential equations which have polynomial solution. The method is based on taking the truncated Chebyshev series expansions of the functions in equation, and then substituting their matrix forms into the result equation. Thereby the given equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients.

Keywords:

• Chebyshev polynomial solutions
• Solutions of certain differential equations

C.R. Categories:

• G.1.7
• G.1.2