Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations

A method for solving the nonlinear second-order Fredholm integro-differential equations is presented. The approach is based on a compactly supported linear semiorthogonal B-spline wavelets. The operational matrices of derivative for B-spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro-differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.