Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

Kamel Al-Khaled, Issam Abu-Irwaq

Abstract


The present article is designed to supply two different numerical
solutions for solving  Kuramoto-Sivashinsky equation. We have made
an attempt to develop a numerical solution via the use of
Sinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sinc
approximations to both derivatives and indefinite integrals reduce
the solution to an explicit system of algebraic equations. The fixed
point theory is used to prove the convergence of the proposed
methods. For comparison purposes, a combination of a Crank-Nicolson
formula in the time direction, with the Sinc-collocation in the
space direction is presented, where the derivatives in the space
variable are replaced by the necessary matrices to produce a system
of algebraic equations. In addition, we present numerical examples
and comparisons to support the validity of these proposed
methods.

Keywords


Kuramoto-Sivashinsky equation, Sinc-Galerkin, Sinc-collocation, Fixed-point iteration

References


F. Stenger, Handbook of Sinc Numerical Methods. Boca Raton, FL: CRC Press, (2010).

F. Stenger, Numerical Methods Based on Sinc and Analytic Functions. Springer-Verlag, New York, (1993).

J. Lund, K.L. Bowers, Sinc methods for quadrature and differential equations, SIAM, Philadelphia, (1992).

Y. Kuramoto, Diffusion-induced chaos in reaction systems,

Suppl. Prog. Theor. Phys., Vol. 64 (1978), Pages 346-367.

Mehrdad Lakestani, Mehdi Dehgan; Numerical solutions of the generalized Kuramoto-Sivashinsky equation using B-spline functions, Appl. Math. Model.,

Vol. 36 (2012), Pages 605-617.




DOI: http://doi.org/10.11591/ijece.v9i5.pp%25p
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