Semiorthogonal B-spline Wavelet for Solving 2D- Nonlinear Fredholm-Hammerstein Integral Equations

Abstract

This work is concerned with the study of the second order (linear) semiorthogonal B-spline wavelet method to solve one-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind. Proof of the existence and uniqueness solution for the two-dimensional Fredholm-Hammerstein nonlinear integral equations of the second kind was introduced. Moreover, generalization the second order (linear) semiorthogonal B-spline wavelet method was achieved and then using it to solve two-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind. This method transform the one-dimensional and two-dimensional nonlinear Fredholm-Hammerstein integral equations of the second kind to a system of algebraic equations by expanding the unknown function as second order (linear) semiorthogonal B-spline wavelet with unknown coefficients. The properties of these wavelets functions are then utilized to evaluate the unknown coefficients. Also some of illustrative examples which show that the second order (linear) semiorthogonal B-spline wavelet method give good agreement with the exact solutions.