Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Nanshan Liu and En-Bing Lin
Pages: [185] - [194]
Received Date: September 5, 2008
Submitted by:
We first introduce an orthogonal basis on [0, 1] generated by Legendre polynomials on [-1, 1], and, then define an associated expansion of an integrable function. We describe some properties and derive a uniform convergence theorem. We further derive the error estimation theorem regarding the expansion. We finally apply them in solving differential equations, integral equations and functional differential equations in several numerical experiments. Our method is more efficient and has better convergence results than some other traditional methods.
Legendre polynomial, associated expansions, orthogonal basis, convergence theorem.
