An Effective Local Radial Basis Function Method for Solving the Delay Volterra Integral Equation of Nonvanishing and Vanishing Types

This paper presents a numerical method for solving a class of the delay Volterra integral equation of nonvanishing and vanishing types by applying the local radial basis function method. This method converts these types of integral equations into an easily solvable system of algebraic equations. To prove the method, we use the discrete collocation method and the local radial basis function method to approximate the delay Volterra integral equation. Also, we use the nonuniform Gauss–Legendre integration method to calculate the integral part appearing in the method. In addition, the existence, uniqueness, and convergence of the solution are investigated in this paper. Finally, some numerical examples are shown to observe the accuracy and effectiveness of the numerical method. Some problems have been plotted and compared with other methods. Obtained numerical results and their comparison with other methods show the reliability and accuracy of this method.