The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves

Authors:
Mehdi Dehghan;Farhad Fakhar-Izadi
Affiliations:
-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

Citing 12
Cited 5

Global properties of pseudospectral methods

Journal of Computational Physics
Numerical Mathematics and Computing

Numerical Mathematics and Computing
Analytical and numerical studies of weakly nonlocal solitary waves of the rotation-modified Korteweg-de Vries equation

Physica D
Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices

Mathematics and Computers in Simulation
Numerical Recipes 3rd Edition: The Art of Scientific Computing

Numerical Recipes 3rd Edition: The Art of Scientific Computing
A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

Mathematics and Computers in Simulation
A novel traveling wave solution for Ostrovsky equation using Exp-function method

Computers & Mathematics with Applications
The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations

Computers & Mathematics with Applications
Solitary waves and fundamental solution for Ostrovsky equation

Mathematics and Computers in Simulation
Conservative numerical schemes for the Ostrovsky equation

Journal of Computational and Applied Mathematics
Solitary wave solutions for a generalized KdV-mKdV equation with variable coefficients

Mathematics and Computers in Simulation
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations

Applied Numerical Mathematics

The use of a Legendre pseudospectral viscosity technique to solve a class of nonlinear dynamic Hamilton-Jacobi equations

Computers & Mathematics with Applications
The Sinc-collocation method for solving the Thomas-Fermi equation

Journal of Computational and Applied Mathematics
A conservative numerical method for the Cahn-Hilliard equation with Dirichlet boundary conditions in complex domains

Computers & Mathematics with Applications
Application of the collocation method for solving nonlinear fractional integro-differential equations

Journal of Computational and Applied Mathematics
Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1+1 nonlinear Schrödinger equations

Journal of Computational Physics

Quantified Score

Hi-index	0.99

Visualization

Abstract

Ostrovsky equation (modified Korteweg-de Vries equation) is used for modeling of a weakly nonlinear surface and internal waves in a rotating ocean. The Ostrovsky equation is a nonlinear partial differential equation and also is complicated due to a nonlinear integral operator as well as spatial and temporal derivatives. In this paper we propose a numerical scheme for solving this equation. Our numerical method is based on a collocation method with three different bases such as B-spline, Fourier and Chebyshev. A numerical comparison of these schemes is also provided by three examples.