Solving higher-order nonlinear Volterra integro-differential equations using two discretization methods

The primary objective of this article is to devis an effective method for solving a high-degree nonlinear Volterra integro-differential equation. First, we conduct a comprehensive literature review to underscore the significance of such mathematical equations in scientific research. Subsequently, we establish sufficient conditions to demonstrate the existence and uniqueness of the exact solution. Then, we employ two different discretization methods, namely Nyström and collocation. Then, we obtain two approximate systems, each of which yields a solution converging to the exact solution. The convergence of these systems is rigorously demonstrated through two theorems. Finally, we present numerical tests to evaluate the effectiveness and simplicity of the proposed numerical processes.