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.
Lakestani, M., Razzaghi, M., & Dehghan, M. (2006). Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations. Mathematical Problems in Engineering, 2006, 1–12. https://doi.org/10.1155/mpe/2006/96184