Numerical Solutions of Third Kind Volterra Integral Equations Using Simpson’s Rule

Volterra integral equations appear when we convert an initial value problem to an integral ‎equation. The solution of the Volterra integral equation is much easier than the original initial value ‎problem. Many problems of thermodynamics, biology, chemistry, medical sciences, physics, ‎heat flow, neutron diffusion problem, electric circuit problem, transform problem mechanics, ‎and engineering can be represented mathematically in terms of Volterra integral equations of the first and ‎second kind. Numerical Method for solving Third Kind Volterra Integral Equations (VIEs) ‎using Simpson's Rule. By approximating the unknown function using Lagrange Polynomial ‎interpolation and applying Simpson's rule for numerical integration, we obtain a system of ‎linear algebraic equations. The solution of this system provides an approximation to the ‎original integral equation‎.