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

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.