The operational matrix of differentiation for orthogonal polynomial series

Abstract

In the present paper a new method is introduced for the approximate solution of ordinary linear differential equations using orthogonal polynomial series on a computer. For this purpose an operational matrix of differentiation is introduced that essentially transforms the differential operation to a matrix multiplication. Additionally, an operational matrix of polynomial series transformation is used that effectively transforms any orthogonal polynomial series to Taylor series. The use of these operational matrices simplifies considerably the structure of the computer codes used for the application of spectral methods for the solution of linear differential equations and allows the generation of a general program for all types of orthogonal polynomial series.