Analysis of stiff systems via the method of generalized orthogonal polynomials

Abstract

The generalized orthogonal polynomials (GOP) which include all types of orthogonal polynomials are applied to the analysis of stiff systems. Using the idea of orthogonal polynomial functions which can be expressed by a power series and vice versa, the integration operational matrix of the GOP is derived. The state variables are expressed in a GOP series. An effective computational algorithm in which the whole time region is divided into several small time intervals is proposed. Only one or two terms of expansion coefficients are enough to get accurate results. The expansion coefficients are only required to be determined at the first time interval and can be used in the subsequent time intervals. A very simple recursive formula is developed to calculate the state functions. Four illlustrative examples are given and very satisfactory computational results are obtained.