Meshless formulation to two‐dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence

Abstract

In this study, the singular boundary method (SBM) is employed for the simulation of nonlinear generalized Benjamin–Bona–Mahony–Burgers problem with initial and Dirichlet‐type boundary conditions. The θ‐weighted finite difference method is used to discretize the time derivatives. Then the original equations are split into a system of partial differential equations. A splitting scheme is applied to split the solution of the inhomogeneous governing equation into homogeneous solution and particular solution. To solve this system, the method of particular solution (MPS) in combination with the SBM is used where the SBM is used for homogeneous solution and MPS is used for particular solution. Furthermore, the stability and convergence of the proposed method is conducted. Finally, several numerical examples with different domains are provided and compared with the exact analytical solutions to show the accuracy and efficiency in comparison with existing other methods.

Numerical Solution for Two-Dimensional Nonlinear Klein-Gordon Equation Through Meshless Singular Boundary Method

“…In this paper, subtracting and adding-back (SAB) technique is a popular approach to calculate the OIFs. In recent years, some famous problems are solved by SBM [19][20][21][22][23].…”

Spectral Method for One Dimensional Benjamin-Bona-Mahony-Burgers Equation Using the Transformed Generalized Jacobi Polynomial

“…Zarebnia et al [29] used the cubic B-spline collocation methods to solve the BBMBE. Aslefallah et al [6] studied the singular boundary method for the simulation of nonlinear generalized BBMB problem with initial and Dirichlet-type boundary conditions. Arora et al [5] developed a hybrid numerical technique combining quintic Hermite collocation method with weighted finite difference scheme to solve the BBMBE.…”