Author(s)

D. Ngo-Cong, N.Mai-Duy, W. Karunasena & T. Tran-Cong

Abstract

This paper presents a new numerical procedure for time-dependent problems. The partition of unity method is employed to incorporate the moving least square and one-dimensional integrated radial basis function networks (MLS-1D-IRBFN) techniques in an approach that produces a very sparse system matrix and offers as a high order of accuracy as that of global 1D-IRBFN method. Moreover, the proposed approach possesses the Kronecker-δ property which helps impose the essential boundary condition in an exact manner. Spatial derivatives are discretised using Cartesian grids and MLS-1D-IRBFN, whereas temporal derivatives are discretised using high-order time-stepping schemes, namely standard θ and fourth-order Runge–Kutta methods. Several numerical examples including twodimensional diffusion equation, one-dimensional advection-diffusion equation and forced vibration of a beam are considered. Numerical results show that the current methods are highly accurate and efficient in comparison with other published results available in the literature. Keywords: time-dependent problems, integrated radial basis functions, moving least square, partition of unity, Cartesian grids.

Keywords

time-dependent problems, integrated radial basis functions, moving least square, partition of unity, Cartesian grids