The solution of initial-boundary value problems with non-local boundary conditions using exponential basis functions

Abstract

In this paper we extend the formulation of a meshless method based on using exponential basis functions (EBFs) to solve heat conduction and wave propagation problems with non-local boundary conditions. This method has been recently employed in the solution of a wide range of initial-boundary value problems with classical boundary conditions. Using a summation of EBFs satisfying the differential equation as well as a novel collocation technique are two main features of the presented method. The proposed method can be easily employed for both one (1D) and two (2D) dimensional problems with non-local boundary conditions. In the section of numerical examples, the capabilities of the presented approach are investigated through the solution of five sample problems. An accuracy indicator is also proposed for assessment of the approximate solution in problems without analytical solution.