An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space - Dai, Xuefei; Niu, Jing; Xu, Yanxin (Journal of applied mathematics & computing, 2023)
The main purpose of this paper is to approximate the solution of the nonlinear Volterra integral equation numerically in the reproducing kernel space. Consequently, in the study, combining Quasi-Newton’s method and the least-square method, we develop a new method for solving this kind of equation. This technique transforms the nonlinear Volterra integral equation into a linear algebraic system of equations, which can be solved by using the least-square method breezily. At the same time, to ensure the preciseness of the method, we strictly analyze the existence and uniqueness of ε -approximate solution and its convergence. Finally, we illustrate the accuracy and reliability of this method by giving some examples.