Legendre Wavelet Method for Numerical Solutions of Partial Differential Equations

We introduce all orthogonal basis oil the square [-1, 1] x [-1, 1] generated by Legendre polynomials oil [-1, 1], and define an associated expression for the expansion of a Riemann integrable function. We describe some properties and derive a uniform convergence theorern. We then present several numerical experiments that indicate that our methods are more efficient and have better convergence results than some other methods. (C) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 26: 81-94, 2010