Convergence and numerical solution of nonlinear generalized Benjamin–Bona–Mahony–Burgers equation in 2D and 3D via generalized finite difference method
A. García, Mihaela Negreanu, Francisco Ureña, A.M. Vargas
Abstract
In this paper we present an application of the Generalized Finite Difference Method to solve the generalized nonlinear Benjamin–Bona–Mahony–Burgers equation in 2D and 3D. We provide two approaches to solving the BBMB equation. First, we directly use the explicit GFD scheme, and second, we transform the equation into a PDE system. In a further attempt we find criteria for the convergence of the fully explicit method using GFDM for the Benjamin–Bona–Mahony–Bourgers equation in 2D and 3D.
Topics & Concepts
MathematicsBurgers' equationConvergence (economics)Nonlinear systemMathematical analysisFinite difference methodApplied mathematicsFinite differencePartial differential equationPhysicsQuantum mechanicsEconomicsEconomic growthNonlinear Waves and SolitonsFractional Differential Equations SolutionsNumerical methods for differential equations