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

DOI10.1002/num.22426OpenAlexW2970135583WikidataQ127313911 ScholiaQ127313911MaRDI QIDQ6071647

Saeid Abbasbandy, Mohammad Aslefallah, Elyas Shivanian

Publication date: 28 November 2023

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

Full work available at URL: https://doi.org/10.1002/num.22426

zbMATH Keywords

stabilityconvergencefundamental solutionsingular boundary methodmethod of particular solutionnonlinear generalized Benjamin-Bona-Mahony-Burgers equation

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

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A new highly accurate numerical scheme for Benjamin-Bona-Mahony-Burgers equation describing small amplitude long wave propagation

Cites Work

• Unnamed Item
• Infinite domain potential problems by a new formulation of singular boundary method
• Solution of potential flow problems by the modified method of fundamental solutions: formulations with the single layer and the double layer fundamental solutions
• Combination of meshless local weak and strong (MLWS) forms to solve the two-dimensional hyperbolic telegraph equation
• A new boundary meshfree method with distributed sources
• A meshless method for two-dimensional diffusion equation with an integral condition
• Singular boundary method for modified Helmholtz equations
• Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions
• The Trefftz method using fundamental solutions for biharmonic equations
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• New periodic and soliton solutions for the generalized BBM and Burgers-BBM equations
• Regularized method of fundamental solutions for boundary identification in two-dimensional isotropic linear elasticity
• Some new solitonary solutions of the modified Benjamin-Bona-Mahony equation
• The first integral method for modified Benjamin-Bona-Mahony equation
• The method of fundamental solutions for inverse boundary value problems associated with the two-dimensional biharmonic equation
• An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation
• Approximate general and explicit solutions of nonlinear BBMB equations by exp-function method
• The method of fundamental solutions for elliptic boundary value problems
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Radial basis functions as approximate particular solutions: Review of recent progress
• A meshless, integration-free, and boundary-only RBF technique
• Meshless local Petrov-Galerkin (MLPG) method for three-dimensional nonlinear wave equations via moving least squares approximation
• More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI)
• Explicit empirical formula evaluating original intensity factors of singular boundary method for potential and Helmholtz problems
• Numerical investigation on convergence rate of singular boundary method
• A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms
• Particular solutions of Helmholtz-type operators using higher order polyharmonic splines
• Some recent results and proposals for the use of radial basis functions in the BEM
• Fast multipole accelerated singular boundary method for the 3D Helmholtz equation in low frequency regime
• A novel meshless method for fully nonlinear advection-diffusion-reaction problems to model transfer in anisotropic media
• Heritage and early history of the boundary element method
• Analytical evaluation of the origin intensity factor of time-dependent diffusion fundamental solution for a matrix-free singular boundary method formulation
• The use of interpolating element-free Galerkin technique for solving 2D generalized Benjamin-Bona-Mahony-Burgers and regularized long-wave equations on non-rectangular domains with error estimate
• Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions
• The numerical solution of nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation via the meshless method of radial basis functions
• The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation in arbitrary domains
• Novel meshless method for solving the potential problems with arbitrary domain
• Investigation on near-boundary solutions by singular boundary method
• THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS
• A survey of applications of the MFS to inverse problems
• Potential Problems by Singular Boundary Method Satisfying Moment Condition
• A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method
• Element‐free Galerkin methods
• Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method
• Stability and convergence of spectral radial point interpolation method locally applied on two‐dimensional pseudoparabolic equation
• Local radial basis function interpolation method to simulate 2D fractional‐time convection‐diffusion‐reaction equations with error analysis
• Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains