A radial basis function (RBF)-finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves

DOI10.1002/num.23077MaRDI QIDQ6556886

Mostafa Abbaszadeh, Alireza Bagheri Salec, Taghreed Abdul-Kareem Hatim Aal-Ezirej

Publication date: 17 June 2024

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

stability analysissolitary wavesradial basis functions (RBFs)convergence and error analysisimproved Boussinesq model (IBM)RBFs-finite difference (RBFs-FD) approach

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) PDEs in connection with fluid mechanics (35Q35) Finite difference methods applied to problems in fluid mechanics (76M20) Solitary waves for incompressible inviscid fluids (76B25) Fixed-point theorems (47H10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical interpolation (65D05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Soliton solutions (35C08) Numerical radial basis function approximation (65D12)

Cites Work

• Energy-preserving finite volume element method for the improved Boussinesq equation
• A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains
• A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
• Stable calculation of Gaussian-based RBF-FD stencils
• A not-a-knot meshless method using radial basis functions and predictor-corrector scheme to the numerical solution of improved Boussinesq equation
• Stabilization of RBF-generated finite difference methods for convective PDEs
• A new approach on numerical solutions of the improved Boussinesq type equation using quadratic B-spline Galerkin finite element method
• The interpolating element-free Galerkin method for solving Korteweg-de Vries-Rosenau-regularized long-wave equation with error analysis
• Blow-up solutions of the generalized Boussinesq equation obtained by variational iteration method
• Compactons and solitary wave solutions for the Boussinesq wave equation and its generalized form
• Linear B-spline finite element method for the improved Boussinesq equation
• Partial differential equations and solitary waves theory
• Interpolation in the limit of increasingly flat radial basis functions
• The overlapped radial basis function-finite difference (RBF-FD) method: a generalization of RBF-FD
• A sine-cosine method for handling nonlinear wave equations
• The solution of the Boussinesq equation using the method of lines
• Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method
• The tanh method for traveling wave solutions of nonlinear equations
• Efficient numerical algorithms for the solution of ``good Boussinesq equation in water wave propagation
• Analysis of Ciarlet-Raviart mixed finite element methods for solving damped Boussinesq equation
• Two conservative difference schemes for the generalized Rosenau equation
• A second order numerical scheme for the solution of the one-dimensional Boussinesq equation
• Gaussian RBF-FD weights and its corresponding local truncation errors
• Method of lines solutions of the extended Boussinesq equations
• Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space
• The Adomian decomposition method for solving the Boussinesq equation arising in water wave propagation
• Solitary-wave propagation and interactions for the ‘good’ Boussinesq equation
• Finite element Galerkin method for the “good” Boussinesq equation
• A new conservative fourth‐order accurate difference scheme for solving a model of nonlinear dispersive equations
• Linearized numerical schemes for the Boussinesq equation
• Numerical solutions of the improved boussinesq equation by the galerkin quadratic B-spline finite element method
• Dynamics of modified improved Boussinesq equation via Galerkin Finite Element Method
• Numerical solutions of Boussinesq equation using Galerkin finite element method

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