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- Title
A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves.
- Authors
Abbaszadeh, Mostafa; Bagheri Salec, AliReza; Hatim Aal‐Ezirej, Taghreed Abdul‐Kareem
- Abstract
The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniqueness of solution of the semi‐discrete scheme according to the fixed point theorem. In addition, the unconditional stability and convergence of the semi‐discrete scheme are presented. Then, we construct the fully discrete formulation based upon the radial basis function‐finite difference method. The convergence rate and stability of the fully‐discrete scheme are analyzed. In the end, some examples in 1D and 2D cases are studied to corroborate the capability of the proposed scheme.
- Subjects
BOUSSINESQ equations; FLUID dynamics; RADIAL basis functions
- Publication
Numerical Methods for Partial Differential Equations, 2024, Vol 40, Issue 3, p1
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.23077