Method of Radial Basis Functions for Solving the Partial Integro-Differential Equation of Diffusion with Nonlocal Effects

The authors considered the method of radial basis functions for the numerical solution of the partial integro-differential equation in multidimensional domains. They used a linear combination of radial basis functions at specific center points and a linear combination of polynomial basis functions to approximate the problem’s solution. The authors proposed the distribution of center points for two and three-dimensional domains. Collocating at the center points leads to the semi-discretized system that contains integral coefficients. Integral coefficients are calculated numerically using the Gauss–Legendre and trapezoidal quadrature rules. A shape parameter is determined using a real-coded genetic algorithm. Numerical results in two- and three-dimensional domains confirm the efficiency of the proposed approach.