A Numerical Method for Fredholm Integro-Differential Equation using Positive Definite Radial Kernels and A Study of the Effect of The Shape Parameter (original) (raw)

In this paper, we use two radial kernels, the Generalized Multiquadrics and the linear Laguerre-Gaussians for the formulation of radial kernel collocation method for solving problems involving Fredholm integro-differential equations. The effect of the shape parameter contained in each of the kernels, on the accuracy of the method is investigated. The method is demonstrated using two examples the numerical results displayed in form of tables and graphs. MATLAB 2018a was used for the implementation.