Gardner Denkleminin Trigonometrik Kuintik B-spline Kolokasyon Yöntemi ile Nümerik Çözümleri

Year 2018, Volume: 22 Issue: 6, 1576 - 1584, 01.12.2018

Özlem Ersoy Hepson

https://doi.org/10.16984/saufenbilder.342571

Cited By: 5

Abstract

Bu çalışmanın
amacı çeşitli disiplinlerde sıkça kullanılan Gardner denkleminin nümerik
çözümlerini elde etmektir. Bu amaç için geniş kararlılık bölgesine sahip
olmasından dolayı klasik Crank-Nicolson yöntemi ile zaman integrasyonu
yapılmıştır. Konum ayrıştırması ise trigonometrik quintik B-spline
fonksiyonları kullanılarak yapılmıştır. Bu yüzden Gardner denklemi beş bant
matris sistemine dönüştürülmüş ve Thomas algoritması uygulanmıştır.

Keywords

Gardner denklemi , trigonometrik quintik B-spline , kolokasyon

Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method

Abstract

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.

Keywords

Gardner Equation , trigonometric quintic B-spline , collocation , wave generation

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