More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI)

Abstract

In this article, the spectral meshless radial point interpolation (SMRPI) technique is applied to the nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) in two-dimension with initial and Dirichlet-type boundary conditions. This method is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. To treat the nonlinearity part, a kind of predictor-corrector scheme combined with Crank-Nicolson technique is adopted. We prove that the time discrete scheme is stable respect to the time variable in H1 and convergent with convergence order O(δt). To show the high accuracy of SMRPI, a comparison study of the present method and recently applied interpolating element-free Galerkin technique is given through applying on GBBMB equation. The results reveal that the method is more accurate and possesses low complexity.