Wavelet-Galerkin method for integro-differential equations

While wavelets have proved effective in signal and image processing, the utility of wavelets in the numerical solutions of differential equations is currently being studied by several investigators. In the place of conventional Fourier or Legendre bases, wavelet bases are tried in the application of spectral methods. In this paper, we consider the application of wavelet bases to the solution of integro-differential equations which are not as extensively studied as differential equations. A new four dimensional connection coefficient arises in the procedure. We describe an algorithm for its computation. Two simple pedagogic nonlinear integro-differential equations are presented as test cases to show that the wavelet bases give accurate results, (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.