Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1576 - 1584 2018-12-01

Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method
Gardner Denkleminin Trigonometrik Kuintik B-spline Kolokasyon Yöntemi ile Nümerik Çözümleri

Özlem Ersoy Hepson [1]

217 383

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.

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.

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Birincil Dil en
Konular Matematik
Yayımlanma Tarihi December 2018
Dergi Bölümü Araştırma Makalesi
Yazarlar

Orcid: orcid.org/0000-0002-5369-8233
Yazar: Özlem Ersoy Hepson
Ülke: Turkey


Bibtex @araştırma makalesi { saufenbilder342571, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1576 - 1584}, doi = {10.16984/saufenbilder.342571}, title = {Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method}, key = {cite}, author = {Ersoy Hepson, Özlem} }
APA Ersoy Hepson, Ö . (2018). Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method. Sakarya University Journal of Science, 22 (6), 1576-1584. DOI: 10.16984/saufenbilder.342571
MLA Ersoy Hepson, Ö . "Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method". Sakarya University Journal of Science 22 (2018): 1576-1584 <http://www.saujs.sakarya.edu.tr/issue/31266/342571>
Chicago Ersoy Hepson, Ö . "Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method". Sakarya University Journal of Science 22 (2018): 1576-1584
RIS TY - JOUR T1 - Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method AU - Özlem Ersoy Hepson Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.342571 DO - 10.16984/saufenbilder.342571 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1576 EP - 1584 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.342571 UR - http://dx.doi.org/10.16984/saufenbilder.342571 Y2 - 2018 ER -
EndNote %0 Sakarya University Journal of Science Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method %A Özlem Ersoy Hepson %T Numerical Solutions of the Gardner Equation via Trigonometric Quintic B-spline Collocation Method %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.342571 %U 10.16984/saufenbilder.342571
ISNAD Ersoy Hepson, Özlem . "Gardner Denkleminin Trigonometrik Kuintik B-spline Kolokasyon Yöntemi ile Nümerik Çözümleri". Sakarya University Journal of Science 22 / 6 (Aralık 2018): 1576-1584. http://dx.doi.org/10.16984/saufenbilder.342571