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

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 eq...

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Bibliographic Details
Published in:Numerical methods for partial differential equations Vol. 36; no. 2; pp. 249 - 267
Main Authors: Aslefallah, Mohammad, Abbasbandy, Saeid, Shivanian, Elyas
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.03.2020
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Subjects:
Boundary conditions
Computer simulation
Convergence
Dirichlet problem
Exact solutions
Finite difference method
fundamental solution
Meshless methods
method of particular solution
nonlinear generalized Benjamin–Bona–Mahony–Burgers equation
Partial differential equations
singular boundary method
stability
Stability analysis
ISSN:0749-159X, 1098-2426
Online Access:Get full text
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Summary: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.
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ISSN:0749-159X
1098-2426
DOI:10.1002/num.22426