Numerical solutions of the Kawahara type equations using radial basis functions

DOI10.1002/num.20633zbMath1242.65207OpenAlexW2132173082MaRDI QIDQ2885160

Yılmaz Dereli, Idris Daǧ

Publication date: 21 May 2012

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

Full work available at URL: https://doi.org/10.1002/num.20633

zbMATH Keywords

collocation methodnumerical examplesradial basis functionsmeshless methodKawahara equationKorteweg-de Vriestravelling wave solution

Mathematics Subject Classification ID

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

Related Items (12)

Nonic B-spline algorithms for numerical solution of the Kawahara equation ⋮ Bell-shaped soliton solutions and travelling wave solutions of the fifth-order nonlinear modified Kawahara equation ⋮ A composite method based on delta‐shaped basis functions and Lie group high‐order geometric integrator for solving Kawahara‐type equations ⋮ Numerical solution by quintic B-spline collocation finite element method of generalized Rosenau-Kawahara equation ⋮ A Legendre dual-Petrov-Galerkin spectral element method for the Kawahara-type equations ⋮ Fourier splitting method for Kawahara type equations ⋮ Highly efficient approach to numerical solutions of two different forms of the modified Kawahara equation via contribution of two effective methods ⋮ Well-posedness of the classical solutions for a Kawahara-Korteweg-de Vries-type equation ⋮ Numerical approximation of modified Kawahara equation using kernel smoothing method ⋮ On the solutions for a Benney-Lin type equation ⋮ Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate ⋮ Global H4 solution for the fifth-order Kudryashov–Sinelshchikov–Olver equation

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 numerical comparison of a Kawahara equation
• Crank-Nicolson - differential quadrature algorithms for the Kawahara equation
• Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
• Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method
• Existence of perturbed solitary wave solutions to a model equation for water waves
• Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• An explicit and numerical solutions of some fifth-order KdV equation by decomposition method
• Compacton solutions of the Kawahara-type nonlinear dispersive equation.
• New exact travelling wave solutions for the Kawahara and modified Kawahara equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• The Korteweg-de Vries-Kawahara equation in a bounded domain and some numerical results
• A note on the homogeneous balance method
• A dual-Petrov-Galerkin method for the Kawahara-type equations
• Doubly periodic solutions of the modified Kawahara equation
• Extended tanh-function method and its applications to nonlinear equations
• Approximate Equations for Long Nonlinear Waves on a Viscous Fluid
• Solitary wave solutions of nonlinear wave equations
• The tanh method: II. Perturbation technique for conservative systems
• Compactons: Solitons with finite wavelength
• Finite amplitude side-band stability of a viscous film
• An analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method

This page was built for publication: Numerical solutions of the Kawahara type equations using radial basis functions