Legendre expansion method for the solution of the second- and fourth-order elliptic equations
This paper presents a formula expressing Legendre polynomials in terms of their derivatives and a formula expressing a Legendre polynomial integrated k-times in terms of Legendre polynomials. In view of these formulae, the second- and fourth-order elliptic equation were solved. Moreover, the suggested method is applicable for a wide area of differential equations. The present results are in satisfactory agreement with the exact solutions. (C) 2002 IMACS. Published by Elsevier Science B.V All rights reserved.
legendre polynomials spectral methods helmholtz equation biharmonic equations