The main purpose of this paper is to get the numerical solutions of the Gardner equation which are widely used in various disciplines. For this purpose, the time integration of the system is achieved by the classical Crank-Nicolson method owing to its large stability region. Space discretization is done by using the trigonometric quintic B-spline functions. Thus the Gardner equation turns into a penta diagonoal matrix equation and the Thomas algorithm is applied.
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Özlem Ersoy Hepson (2018) studied this question.
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