Element-free approximation of generalized regularized long wave equation
type: Item
instance of: scholarly article
title: Element-free approximation of generalized regularized long wave equation
zbMATH Open document ID: 1407.76063
DOI: 10.1155/2014/206017
author: Dongmei Huang
author: L. W. Zhang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The generalized regularized long wave (GRLW) equation is an important nonlinear equation for describing a large number of physical phenomena, for examples, the shallow water waves and plasma waves. In this study, numerical approximation of the GRLW using the element-free improved moving least-squares Ritz (IMLS-Ritz) method is performed. In the solution procedure, the IMLS approximation is employed to reduce the number of unknown coefficients in the trial functions. The Ritz minimization procedure is then used to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear GRLW equation. Time difference technique and Newton-Raphson method are adopted to solve the nonlinear equation system. Numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element-free IMLS-Ritz method by comparing the computed IMLS-Ritz results with the existing available analytical solutions.
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 82D10
zbMATH DE Number: 7015905
Wikidata QID: Q59063772
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/206017
OpenAlex ID: W2119580617
cites work: Long waves on a beach
cites work: Effects of convection on a modified GRLW equation
cites work: On the stability of solitary-wave solutions of model equations for long waves
cites work: A finite difference scheme for generalized regularized long-wave equation
cites work: A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation.
cites work: An application of the decomposition method for the generalized KdV and RLW equations
cites work: Least-squares quadratic B-spline finite element method for the regularised long wave equation
cites work: A B‐spline finite element method for the regularized long wave equation
cites work: A least-squares finite element scheme for the RLW equation
cites work: Application of cubic B-splines for numerical solution of the RLW equation
cites work: Collocation solution for RLW equation with septic spline
cites work: A collocation method with cubic B-splines for solving the MRLW equation
cites work: Q4360591
cites work: A Petrov-Galerkin method for solving the generalized regularized long wave (GRLW) equation
cites work: Numerical analysis of generalized regularized long wave equation using the element-free kp-Ritz method
cites work: Analyzing modified equal width (MEW) wave equation using the improved element-free Galerkin method
cites work: Exact solutions and invariants of motion for general types of regularized long wave equations
cites work: Geometric nonlinear meshless analysis of ribbed rectangular plates based on the FSDT and the moving least-squares approximation
cites work: An improved interpolating element-free Galerkin method based on nonsingular weight functions
cites work: The interpolating element-free Galerkin method for 2D transient heat conduction problems
cites work: The improved moving least-square Ritz method for the one-dimensional sine-Gordon equation
cites work: The interpolating boundary element-free method for unilateral problems arising in variational inequalities
cites work: Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems
cites work: Element‐free Galerkin methods
cites work: An introduction to SPH
cites work: Q4781993
cites work: Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method
cites work: Large deflection geometrically nonlinear analysis of carbon nanotube-reinforced functionally graded cylindrical panels
cites work: A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
cites work: Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells.
cites work: Mesh-free radial basis function method for buckling analysis of non-uniformly loaded arbitrarily shaped shear deformable plates.
cites work: Postbuckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach
cites work: A meshfree method for the numerical solution of the RLW equation
cites work: Galerkin method for the numerical solution of the RLW equation using quintic B-splines
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description: scientific article; zbMATH DE number 7015905