THE USE OF GENERALIZED LAGUERRE-POLYNOMIALS IN SPECTRAL METHODS FOR NONLINEAR DIFFERENTIAL-EQUATIONS

The expansion of products of generalized Laguerre polynomials L-n(v)(x ) in terms of a series of generalized Laguerre polynomials is consider ed. The expansion coefficients, which are equal to triple-product inte grals of generalized Laguerre polynomials, are expressed in terms of a three-index recurrence relation. This is reduced to a one-index relat ion which facilitates computation of the expansion coefficients. The r esults are useful in the solution of nonlinear differential equations when it is desired to express products of generalized Laguerre polynom ials as a linear series of these functions. As an application, we use the results to compute a spectral solution of a nonlinear boundary-val ue problem, namely the Blasius equation on a semi-infinite interval. B y using a truncated series containing the first eight polynomials L-n( 1/2)(x), a solution is obtained within 4% accuracy. (C) 1998 Elsevier Science Ltd. All rights reserved.