Meshless formulation to two‐dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence. Issue 2 (30th August 2019)

• Record Type: Journal Article
• Authors: Aslefallah, Mohammad; Abbasbandy, Saeid; Shivanian, Elyas
• Is Part Of: Numerical methods for partial differential equations. Volume 36:Issue 2(2020)
• Page Start: 249
• Page End: 267
• Publication Date: 2019-08-30
• Subjects: convergence -- fundamental solution -- method of particular solution -- nonlinear generalized Benjamin–Bona–Mahony–Burgers equation -- singular boundary method -- stability; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22426
• Languages: English
• ISSNs: 0749-159X

Abstract

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.