A shift‐adaptive meshfree method for solving a class of initial‐boundary value problems with moving boundaries in one‐dimensional domain

DOI10.1002/num.22081zbMath1354.65203OpenAlexW2534498687MaRDI QIDQ5298302

Gholamreza Garmanjani, Mohsen Esmaeilbeigi

Publication date: 14 December 2016

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

Full work available at URL: https://doi.org/10.1002/num.22081

zbMATH Keywords

algorithmstabilitynumerical examplefinite difference schememoving boundariesmeshless methodKansa's methodregularized long-wave equationradial basis function collocationmultiquadricKorteweg-de Vries problemshifted node adaptive

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Higher-order nonlinear hyperbolic equations (35L75)

Related Items (5)

Adaptive residual Refinement in an RBF Finite difference scheme for 2D time-dependent problems ⋮ An RBF-PUM finite difference scheme for forward-backward heat equation ⋮ On the convergence analysis and stability of the RBF-adaptive method for the forward-backward heat problem in 2D ⋮ A RBF partition of unity collocation method based on finite difference for initial-boundary value problems ⋮ Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation

Uses Software

• MOVCOL

Cites Work

• Unnamed Item
• Parametric spline solution of the regularized long wave equation
• A new approach based on the genetic algorithm for finding a good shape parameter in solving partial differential equations by Kansa's method
• A meshfree method for numerical solution of KdV equation
• Application of meshfree collocation method to a class of nonlinear partial differential equations
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Stabilization of RBF-generated finite difference methods for convective PDEs
• Moving mesh methods with upwinding schemes for time-dependent PDEs
• Dynamically knots setting in meshless method for solving time-dependent propagations equation
• A dynamic meshless method for the least squares problem with some noisy subdomains
• A radial basis collocation method for Hamilton-Jacobi-Bellman equations
• KdV equation in domains with moving boundaries
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Adaptive greedy techniques for approximate solution of large RBF systems
• Grid-free adaptive semi-Lagrangian advection using radial basis functions
• Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier-Stokes equations
• An adaptive node regeneration technique for the efficient solution of elasticity problems using MDLSM method
• Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations
• Adaptive radial basis function methods for time dependent partial differential equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• An adaptive greedy algorithm for solving large RBF collocation problems
• A moving collocation method for solving time dependent partial differential equations
• The parameter \(R^ 2\) in multiquadric interpolation
• Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation
• Adaptive residual subsampling methods for radial basis function interpolation and collocation problems
• A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation
• A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries
• Dynamic node adaptive strategy for nearly singular problems on large domains
• Moving collocation method for a reaction-diffusion equation with a traveling heat source
• A large time‐step implicit moving mesh scheme for moving boundary problems
• The second‐order upwind finite difference fractional steps method for moving boundary value problem of oil‐water percolation
• Convergence of the Adomian decomposition method for initial-value problems
• Domain decomposition for time-dependent problems using radial based meshless methods
• Radial basis collocation method and quasi-Newton iteration for nonlinear elliptic problems
• A meshless method using the radial basis functions for numerical solution of the regularized long wave equation
• Node adaptive domain decomposition method by radial basis functions
• Scattered Data Interpolation: Tests of Some Method
• An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations
• A moving mesh method in multiblock domains with application to a combustion problem
• Adaptive local grid refinement algorithms for finite‐element collocation
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Adaptive wavelet frame domain decomposition methods for nonlinear elliptic equations
• A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs

This page was built for publication: A shift‐adaptive meshfree method for solving a class of initial‐boundary value problems with moving boundaries in one‐dimensional domain