Numerical solution, convergence and stability of error to solve quadratic mixed integral equation

Abstract

The main goal of this document is to demonstrate the existence of a unique solution and determine the computational solution of the Quadratic mixed integral equation of Volterra Fredholm type (QMIE) of (2 + 1) dimensional in the space \({L}_{2}([0,a]\times [0,b])\times C[0,T],(T<1).\) Banach’s fixed-point hypothesis describes questions regarding the existence of the solution as well as its uniqueness. Furthermore, we discuss the convergence of the solution and the stability of the numerical solution’s error. QMIE ultimately results in a set of Quadratic integral equations in position when the quadratic numerical approach is used. Then, using the orthogonal polynomial technique while applying the Jacobi polynomial method, we obtain a nonlinear algebraic system of equations. Several illustrative examples in numerical form are shown below to explain the procedures and all the numerical outcomes are calculated and the corresponding errors are computed according to the Maple 18 program.