Rational Laguerre Functions And Their Applications

Abstract

In this work, we introduce a new class of rational basis functions defined on [ , ) a b and based on mapping the Laguerre polynomials on the bounded domain [ , ) a b . By using these rational functions as basic functions, we implement spectral methods for numerical solutions of operator equations. Also the quadrature formulae and operational matrices (derivative, integral and product) with respect to these basis functions are obtained. We show that using quadrature formulae based on rational Laguerre functions give us very good results for numerical integration of rational functions and also implementing spectral methods based on these basis functions for solving stiff systems of ordinary differential equationsgive us suitable results. The details of the convergence rates of these basis functions for the solutions of operator equations are carried out, both theoretically and computationally and the error analysis is presented in   2 [ , ) L a b space norm.