Numerical solutions of non-linear volterra integral equations of the second kind

In this thesis it will be shown how one can solve one of the types of integral equation, non-linear Volterra Integral Equations (VIEs) of the second kind, by certain methods: numerical integration (Trapezoidal rule and Simpson's rule), Runge-Kutta methods (classic third-order, optimal third-order, fourth-order, and classic fourth-order), classic spline functions (quadratic and cubic classic spline functions), and B-spline functions (first-order, second-order, third-order, and fourth-order). It will also be shown how one can convert one of the methods to another one. These methods exist and are easy to use to solve differential equations and integration problems, but it is difficult to apply them to integral equations, especially non-linear integral equations, because the known function occurs into kernel of the integral. Therefore it is needed to modify these methods and techniques to apply them to non-linear integral equations.