Haar Wavelet Method for the Numerical Solution of Nonlinear Fredholm Integro-Differential Equations

The solution of nonlinear Fredholm integro-differential equations plays a significant role in analyzing many nonlinear events that occur in chemistry, physics, mathematical biology, and a variety of other fields of science and engineering. A physical event can be represented by a differential equation, an integro-differential equation since many of these equations cannot be solved directly or it is difficult to solve. Numerical approaches that are useful combinations of numerical integration must frequently be used. This work presents a method for solving the type of nonlinear Fredholm integro-differential equation (NFIDE) of the second kind. The Leibnitz rule is used with the Haar wavelet collocation method in this paper to solve NFIDE numerically. Some techniques are used to transfer the equation into an algebraic system through an operational matrix. The convergence analysis had been proved through this work and the numerical experiments had been given to illustrate the effectiveness of the proposed method based on MATLAB programming.