An efficient algorithm for solving Volterra integro-differential equations based on Alpert's multi-wavelets Galerkin method

This paper is concerned with the application of the multi-wavelets Galerkin method to linear and nonlinear second order Volterra integro-differential equations. Using the operational matrices of integration and wavelet transform matrix, we reduce the problem to a set of algebraic equations. For linear type, we use thresholding to reduce the computational effort. We demonstrate that our solutions may be efficiently represented in a multi-wavelets basis, due to flexible vanishing moments property of this type of multi-wavelets. The L2 convergence of the scheme for the proposed equation has been investigated. A series of numerical tests is provided to demonstrate the validity and applicability of the technique.