Legendre expansion method for the solution of the second-and fourth-order elliptic equations

Elsayed M.E. Elbarbary

Mathematics and Computers in Simulation (MATCOM), 2002, vol. 59, issue 5, 389-399

Abstract: 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.

Keywords: Legendre polynomials; Spectral methods; Helmholtz equation; Biharmonic equations (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:59:y:2002:i:5:p:389-399

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