On existence and numerical solution of higher order nonlinear integro-differential equations involving variable coefficients

Abstract

We investigate the approximate solution to a class of fourth-order Volterra–Fredholm integro differential equations (VFIDEs). Additionally, we are able to get some adequate results for the existence of a solution with the use of nonlinear analysis techniques. The basis for the required numerical computation is provided by the Haar wavelet collocations (HWCs) technique, which converts the problems into a system of algebraic equations. Then, in order to obtain the required numerical solution, we solve the resulting system of algebraic equations using Gauss elimination and Broyden’s techniques. This method can be used to show convergence, and the predicted rate of convergence is two. Along with relevant examples, we have included a graphical presentation to demonstrate our suggested approach.