DOI
10.34229/KCA2522-9664.24.4.10
UDC 519.6
METHOD OF RADIAL BASIS FUNCTIONS FOR A PARTIAL
INTEGRO-DIFFERENTIAL EQUATION OF DIFFUSION WITH NON-LOCAL EFFECTS
Abstract. The method of radial basis functions for the numerical solution of the partial integro-differential equation in multi-dimensional domains is considered. A linear combination of radial basis functions at specific center points and a linear combination of polynomial basis functions are employed to approximate the problem’s solution. The distribution of the center points is proposed for both 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 by a real-coded genetic algorithm. Numerical results both in two- and three-dimensional domains confirm the applicability of the proposed approach.
Keywords: elliptic partial integro-differential equation, radial basis functions, polynomial basis, genetic algorithm.
full text
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