saujs Sakarya University Journal of Science 2147-835X Sakarya University 10.16984/saufenbilder.342571 Mathematical Sciences Matematik Gardner Denkleminin Trigonometrik Kuintik B-spline Kolokasyon Yöntemi ile Nümerik Çözümleri Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method Ersoy Hepson Özlem 12 01 2018 22 6 1576 1584 10 10 2017 03 11 2018 Copyright © 1997, Sakarya University Journal of Science 1997 Sakarya University Journal of Science

Bu çalışmanınamacı çeşitli disiplinlerde sıkça kullanılan Gardner denkleminin nümerikçözümlerini elde etmektir. Bu amaç için geniş kararlılık bölgesine sahipolmasından dolayı klasik Crank-Nicolson yöntemi ile zaman integrasyonuyapılmıştır. Konum ayrıştırması ise trigonometrik quintik B-splinefonksiyonları kullanılarak yapılmıştır. Bu yüzden Gardner denklemi beş bantmatris sistemine dönüştürülmüş ve Thomas algoritması uygulanmıştır.

The main purpose of this paper is to get the numericalsolutions of the Gardner equation which are widely used in various disciplines.For this purpose, the time integration of the system is achieved by theclassical Crank-Nicolson method owing to its large stability region. Spacediscretization is done by using the trigonometric quintic B-spline functions.Thus the Gardner equation turns into a penta diagonoal matrix equation and theThomas algorithm is applied.

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