A meshless method using the radial basis functions for numerical solution of the regularized long wave equation

DOI10.1002/num.20457zbMath1195.65142OpenAlexW2017120543WikidataQ115398473 ScholiaQ115398473MaRDI QIDQ3576816

Mehdi Dehghan, Ali Shokri

Publication date: 3 August 2010

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

Full work available at URL: https://doi.org/10.1002/num.20457

zbMATH Keywords

algorithmnumerical examplesregularized long wave equationcollocationpredictor-correctorthin plate splines radial basis functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Higher-order nonlinear hyperbolic equations (35L75)

Related Items

Local radial basis functions and scale-3 Haar wavelets operational matrices based numerical algorithms for generalized regularized long wave model, Conservative difference scheme of solitary wave solutions of the generalized regularized long-wave equation, Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation, An accurate and novel numerical simulation with convergence analysis for nonlinear partial differential equations of Burgers-Fisher type arising in applied sciences, A shift‐adaptive meshfree method for solving a class of initial‐boundary value problems with moving boundaries in one‐dimensional domain, A Legendre spectral element method for the family of regularized long wave equations, Efficient numerical methods for boundary data and right‐hand side reconstructions in elliptic partial differential equations, Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau-Kawahara-RLW equation with generalized Novikov type perturbation, Solitary wave solutions of the nonlinear generalized Pochhammer-Chree and regularized long wave equations, The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis, Optimal error estimate of two linear and momentum‐preserving Fourier pseudo‐spectral schemes for the RLW equation, High-order compact finite difference schemes for solving the regularized long-wave equation, A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation, The conservative and fourth-order compact finite difference schemes for regularized long wave equation, Two conservative difference schemes for a model of nonlinear dispersive equations, A new algorithm for analysis and simulation of (2+1) Korteweg-de Vries-Rosenau-regularized long-wave model, Simulations of dendritic solidification via the diffuse approximate method, Novel Transparent Boundary Conditions for the Regularized Long Wave Equation, The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas, An efficient numerical simulation of nonlinear‐dispersive model of shallow water wave, A Strang splitting approach combined with Chebyshev wavelets to solve the regularized long-wave equation numerically, A differential quadrature method for numerical solutions of Burgers'‐type equations, On the accuracy of some explicit and implicit methods for the inviscid GRLW equation subject to initial Gaussian conditions, Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method, A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation, A meshless finite-point approximation for solving the RLW equation, An image denoising approach based on a meshfree method and the domain decomposition technique, A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation, B-spline quasi-interpolation based numerical methods for some Sobolev type equations, Interpolating element-free Galerkin method for the regularized long wave equation and its error analysis, A two-grid block-centered finite difference method for the nonlinear regularized long wave equation, Delta-shaped basis functions-pseudospectral method for numerical investigation of nonlinear generalized equal width equation in shallow water waves, High-order conservative difference scheme for a model of nonlinear dispersive equations, Orbital stability of solitary waves for the compound KdV equation, A conservative linear difference scheme for the 2D regularized long-wave equation, Solving the generalized regularized long wave equation on the basis of a reproducing kernel space, A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations, A numerical study of rotation effect on the propagation of nonlinear internal solitary waves in the northern South China Sea, Unnamed Item, A meshless method using radial basis functions for the numerical solution of two-dimensional ZK-BBM equation, Time-linearized, compact methods for the inviscid GRLW equation subject to initial Gaussian conditions, The interpolating element-free Galerkin method for solving Korteweg-de Vries-Rosenau-regularized long-wave equation with error analysis, Soliton wave solutions of nonlinear mathematical models in elastic rods and bistable surfaces, Uniform error estimates of fourth-order conservative linearized difference scheme for a mathematical model for long wave

Cites Work

• Unnamed Item
• Unnamed Item
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• A finite difference solution of the regularized long-wave equation
• On the solution of the non-local parabolic partial differential equations via radial basis functions
• A numerical method for KdV equation using collocation and radial basis functions
• Convergence of meshless Petrov-Galerkin method using radial basis functions
• Solving partial differential equations by meshless methods using radial basis functions
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• Meshless local Petrov-Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity
• Numerical study of the regularized long-wave equation. I: Numerical methods
• Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
• An efficient numerical scheme for Burger equation
• Solving partial differential equations by collocation using radial basis functions
• Modelling an undular bore with \(B\)-splines
• Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling
• A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation.
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics
• Numerical comparisons of two meshless methods using radial basis functions
• Collocation solution for RLW equation with septic spline
• The Fourier pseudospectral method with a restrain operator for the RLW equation
• Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions
• Parameter determination in a partial differential equation from the overspecified data
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Solve partial differential equations by meshless subdomains method combined with RBFs
• Solitary waves of the EW and RLW equations
• A computational method for the regularized long wave (RLW) equation
• A Petrov-Galerkin finite element scheme for the regularized long wave equation
• Solitary waves of the regularised long-wave equation
• Numerical solution of regularized long wave equation using Petrov-Galerkin method
• Numerical solution of regularized long-wave equation
• Galerkin method for the numerical solution of the RLW equation using quadratic B-splines
• High-order compact difference scheme for the regularized long wave equation
• Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method
• Euler operators and conservation laws of the BBM equation
• A numerical method for heat transfer problems using collocation and radial basis functions
• A B‐spline finite element method for the regularized long wave equation
• A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations
• New concepts in meshless methods
• Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement
• A numerical solution of the RLW equation by Galerkin method using quartic B‐splines
• A least-squares finite element scheme for the RLW equation
• New solitary wave solutions for generalized regularized long-wave equation
• Stable and unstable solitary-wave solutions of the generalized regularized long-wave equation
• A computational method for regularized long wave equation
• Solitary waves of the splitted RLW equation