## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Chebyshev wavelet collocation method for Ginzburg-Landau equation

**ABSTRACT**

The main aim of this paper is to investigate the efficient Chebyshev wavelet collocation method for Ginzburg-Landau equation. The basic idea of this method is to have the approximation of Chebyshev wavelet series of a non-linear partial differential equation. We demonstrate how to use the method for the numerical solution of the Ginzburg-Landau Equation with initial and boundary conditions. For this purpose, we have obtained operational matrix for Chebyshev wavelets. By applying this technique in Ginzburg-Landau equation, the partial differential equation is converted into an algebraic system of non-linear equations and this system has been solved using Maple computer algebra system. We demonstrate the validity and applicability of this technique which has been clarified by using an example. Exact solution is compared with an approximate solution. Moreover, Chebyshev wavelet collocation method is found to be acceptable, efficient, accurate and computationall for the non-linear or linear partial differential equation.

**KEYWORDS**

PAPER SUBMITTED: 2018-09-20

PAPER REVISED: 2018-10-17

PAPER ACCEPTED: 2018-10-30

PUBLISHED ONLINE: 2018-12-16

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