The numerical solution of non-linear weakly singular Volterra integro-differential equations by Taylor series - Reproducing Kernel Hilbert space method

This article uses the Taylor series-reproducing kernel Hilbert space method to solve nonlinear weakly singular Volterra integro-differential equations. The Taylor series replaces the nonlinear part under the integral sign, transforming the equation into an ordinary differential equation. This type of equation is difficult to solve analytically. The solution methodology is based on generating an orthogonal basis for the functions, which contributes to formulating numerical solutions in the form of a finite series. The results show that the approximate solutions obtained are close to the exact solution, confirming the method's effectiveness as a reliable and practical tool for solving these equations.