Numerical study of high order nonlinear dispersive PDEs using different RBF approaches
From MaRDI portal
Publication:2085674
DOI10.1016/j.apnum.2022.08.007zbMath1504.35447OpenAlexW4292239902WikidataQ114207993 ScholiaQ114207993MaRDI QIDQ2085674
Marjan Uddin, Thabet Abdeljawad, Muhammad Zamir, Hameed Ullah Jan
Publication date: 18 October 2022
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2022.08.007
Korteweg-de Vries equationCamassa-Holm equationDegasperis-Procesi equationRBF-FD methodRBF-PS methodRBFs methods
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Traveling wave solutions (35C07) Numerical radial basis function approximation (65D12)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Recent advances on radial basis function collocation methods
- Conservative finite difference schemes for the Degasperis-Procesi equation
- Fourier spectral methods for Degasperis-Procesi equation with discontinuous solutions
- Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
- A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations
- Adaptive meshless centres and RBF stencils for Poisson equation
- Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations
- Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis-Procesi equation
- Existence, uniqueness and stability for a class of third-order dissipative problems depending on time
- On the well-posedness of the Degasperis-Procesi equation
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Global weak solutions and blow-up structure for the Degasperis-Procesi equation
- On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation
- Formation and dynamics of shock waves in the Degasperis-Procesi equation
- RBF-PS scheme for solving the equal width equation
- Meshfree explicit local radial basis function collocation method for diffusion problems
- Local radial basis function based gridfree scheme for unsteady incompressible viscous flows
- Modified Camassa-Holm and Degasperis-Procesi equations solved by Adomian's decomposition method and comparison with HPM and exact solutions
- The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems
- Miscellaneous error bounds for multiquadric and related interpolators
- Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation
- Meshless methods: An overview and recent developments
- Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
- Global existence for a new periodic integrable equation.
- Local multiquadric approximation for solving boundary value problems
- A high order method for numerical solution of time-fractional KdV equation by radial basis functions
- Numerical solution of a non-classical two-phase Stefan problem via radial basis function (RBF) collocation methods
- Numerical investigation of the time fractional mobile-immobile advection-dispersion model arising from solute transport in porous media
- A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method
- A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompact solutions
- Global weak solutions for a new periodic integrable equation with peakon solutions
- A local radial basis functions -- finite difference technique for the analysis of composite plates
- Solving differential equations with radial basis functions: Multilevel methods and smoothing
- Two-dimensional simulation of the damped Kuramoto-Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization
- New cubic B-spline approximation for solving third order Emden-Flower type equations
- Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method
- The Runge phenomenon and spatially variable shape parameters in RBF interpolation
- Poisson structure and action-angle variables for the Camassa-Holm equation
- Near-corner waves of the Camassa-Holm equation
- Numerical simulation of Camassa-Holm peakons by adaptive upwinding.
- Cartesian grid methods using radial basis functions for solving Poisson, Helmholtz, and diffusion--convection equations
- On the numerical solution of Bagley-Torvik equation via the Laplace transform
- Kernel-based Approximation Methods using MATLAB
- Soliton Kernels for Solving PDEs
- Inverse scattering transform for the Camassa–Holm equation
- From Global to Local Radial Basis Function Collocation Method for Transport Phenomena
- Stability of peakons for the Degasperis-Procesi equation
- Radial Basis Functions
- Stability of peakons
- Spectral Methods in MATLAB
- An integrable shallow water equation with peaked solitons
- Camassa–Holm, Korteweg–de Vries and related models for water waves
- NEW BOUNDED TRAVELING WAVES OF CAMASSA–HOLM EQUATION
- Multivariate Interpolation and Conditionally Positive Definite Functions. II
- A point interpolation meshless method based on radial basis functions
- Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations
- A factorization procedure for solving the Camassa–Holm equation
- A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
- On the Cauchy problem for a generalized Camassa-Holm equation
