Atomic radial basis functions in numerical algorithms for solving boundary-value problems for the Laplace equation

Abstract

A numerical method for solution of boundary-value problems of mathematical physics is described that is based on the use of radial atomic basis functions. Atomic functions are compactly supported solutions of functional-differential equations of special form. The convergence of this numerical method is investigated for the case of using an atomic function in solving the Dirichlet boundary-value problem for the Laplace equation.

Compactly supported functions generated by a polyharmonic operator

“…x x 1 2 [16]. Based on the approaches of [5][6][7][8], a more detailed investigation of characteristic properties of the considered atomic functions can be pursued.…”