Staff Members - Benha University
Fourier spectral methods for solving some nonlinear partial differential equations
The International Journal of Open Problems in Computer Science and Mathematics • 2013
Publication Information
Authors
Hany N. Hassan; Hassan K. Saleh
Keywords
Fourier spectral method, Fast Fourier transform, Boussinesq
equation, Korteweg-de Vries equation; leap frog, finite difference.
Journal
The International Journal of Open Problems in Computer Science and Mathematics
Publisher
Not Available
Volume
6
Issue
2
Pages
Not Available
publication.type
International
Paper Link
Not Available
Supplementary Materials
Not Available
Abstract
The spectral collocation or pseudospectral (PS) methods (Fourier
transform methods) combined with temporal discretization techniques to
numerically compute solutions of some partial differential equations (PDEs). In
this paper, we solve the Korteweg-de Vries (KdV) equation using a Fourier
spectral collocation method to discretize the space variable, leap frog and
classical fourth-order Runge-Kutta scheme (RK4) for time dependence. Also,
Boussinesq equation is solving by a Fourier spectral collocation method to
discretize the space variable, finite difference and classical fourth-order Runge-
Kutta scheme (RK4) for time dependence. Our implementation employs the Fast
Fourier Transform (FFT) algorithm.
transform methods) combined with temporal discretization techniques to
numerically compute solutions of some partial differential equations (PDEs). In
this paper, we solve the Korteweg-de Vries (KdV) equation using a Fourier
spectral collocation method to discretize the space variable, leap frog and
classical fourth-order Runge-Kutta scheme (RK4) for time dependence. Also,
Boussinesq equation is solving by a Fourier spectral collocation method to
discretize the space variable, finite difference and classical fourth-order Runge-
Kutta scheme (RK4) for time dependence. Our implementation employs the Fast
Fourier Transform (FFT) algorithm.