# Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation

Open Mathematics (2012)

- Volume: 10, Issue: 1, page 173-187
- ISSN: 2391-5455

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topUjjwal Koley. "Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation." Open Mathematics 10.1 (2012): 173-187. <http://eudml.org/doc/269610>.

@article{UjjwalKoley2012,

abstract = {We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the standard Fourier-Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L 2-error bound of spectral accuracy in space and of second-order accuracy in time.},

author = {Ujjwal Koley},

journal = {Open Mathematics},

keywords = {Kawahara equation; Fourier-Galerkin spectral method; Error estimate; Convergence; error estimate; convergence; semidiscretization; Korteweg-de Vries-Kawahara equation; periodic solution; leap-frog method; Crank-Nicolson method},

language = {eng},

number = {1},

pages = {173-187},

title = {Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation},

url = {http://eudml.org/doc/269610},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Ujjwal Koley

TI - Error estimate for a fully discrete spectral scheme for Korteweg-de Vries-Kawahara equation

JO - Open Mathematics

PY - 2012

VL - 10

IS - 1

SP - 173

EP - 187

AB - We are concerned with convergence of spectral method for the numerical solution of the initial-boundary value problem associated to the Korteweg-de Vries-Kawahara equation (Kawahara equation, in short), which is a transport equation perturbed by dispersive terms of the 3rd and 5th order. This equation appears in several fluid dynamics problems. It describes the evolution of small but finite amplitude long waves in various problems in fluid dynamics. These equations are discretized in space by the standard Fourier-Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L 2-error bound of spectral accuracy in space and of second-order accuracy in time.

LA - eng

KW - Kawahara equation; Fourier-Galerkin spectral method; Error estimate; Convergence; error estimate; convergence; semidiscretization; Korteweg-de Vries-Kawahara equation; periodic solution; leap-frog method; Crank-Nicolson method

UR - http://eudml.org/doc/269610

ER -

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