Legendre wavelet method for numerical solutions of partial differential equations

We introduce an orthogonal basis on the square [?1, 1] × [‐1, 1] generated by Legendre polynomials on [?1, 1], and define an associated expression for the expansion of a Riemann integrable function. We describe some properties and derive a uniform convergence theorem. We then present several numerical experiments that indicate that our methods are more efficient and have better convergence results than some other methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010