Drinfel’d Sokolov Wilson Sisteminin Diferansiyel Kuadratür ve Sonlu Farklar Metodu Kullanılarak Nümerik Çözümü
Abstract
Bu makalede, Drinfel’d-Sokolov-Wilson sistemi tarafından tanımlanan başlangıç değer probleminin nümerik çözümü incelenmiştir. Sistemdeki denklemler uzayda bir bölge ayrıştırma metodu olan ve az sayıda ayrıştırma noktası ile doğru çözümler verme özelliği olan diferensiyel kuadratür metodu kullanılarak ayrıştırılmıştır. Sonuçta oluşan zaman-bağımlı adi diferansiyel denklemler sistemi daha sonra bir açık-kapalı sonlu farklar metodu ile çözülmüştür. Açık-kapalı bir zaman metodu kullanılarak mümkün olan kararlılık problemleri bertaraf edilmiştir. Önerilen metot nümerik olarak test edilmiştir ve az sayıda ayrıştırma noktası ile yani düşük bir hesaplama maliyeti ile doğru çözümler elde edilmiştir
References
- Drinfel’d, VG., Sokolov, VV. 1985. Lie algebras and equations of Korteweg-de Vries Type, J. Sov. Math., 30:1975-2005.
- Meral, G., Tezer Sezgin, M. 2011. The comparison between the DRBEM and DQM solution of nonlinear reaction- diffusion equation, Commun. in Nonlinear Sci. Numer. Simulat., 16:3990-3995.
- Shu, C. 2000. Differential quadrature and its applications in engineering, Springer, London.
- Wazwaz, AM. 2006. Exact and explicit travelling wave solutions for the nonlinear Drinfeld-Sokolov system, Commun. in Nonlinear Sci. Numer. Simulat., 11:311-325.
- Wilson, G., 1982. The Affine Lie Algebra C11 and an equation of Hirota and Satsuma, Physics Letters, 89A(7):332-334.
- Zhang, WM., 2011. Solitary solutions and singular periodic solutions of the Drinfeld-Sokolov-Wilson equation by variational approach, Applied Mathematical Sciences, 5(38):1887-1894.
Numerical Solution of Drinfel’d Sokolov Wilson System Using Differential Quadrature and Finite Difference Methods
Abstract
In this paper, the numerical solution of the initial value problem defined by the Drinfel’d-Sokolov-Wilson system is investigated. The equations in the system are discretized spatially by using the differential quadrature method DQM which is a domain discretization method and have the property of giving accurate solutions with a small number of discretization points. The resulting time-dependent system of ordinary differential equations is then solved by an explicit-implicit finite difference method FDM . By using an explicit-implicit scheme for the time integration, the possible stability problems are eliminated. The proposed method is tested numerically and accurate solutions of are obtained with a small number of discretization points thus with a low computational cost.
References
- Drinfel’d, VG., Sokolov, VV. 1985. Lie algebras and equations of Korteweg-de Vries Type, J. Sov. Math., 30:1975-2005.
- Meral, G., Tezer Sezgin, M. 2011. The comparison between the DRBEM and DQM solution of nonlinear reaction- diffusion equation, Commun. in Nonlinear Sci. Numer. Simulat., 16:3990-3995.
- Shu, C. 2000. Differential quadrature and its applications in engineering, Springer, London.
- Wazwaz, AM. 2006. Exact and explicit travelling wave solutions for the nonlinear Drinfeld-Sokolov system, Commun. in Nonlinear Sci. Numer. Simulat., 11:311-325.
- Wilson, G., 1982. The Affine Lie Algebra C11 and an equation of Hirota and Satsuma, Physics Letters, 89A(7):332-334.
- Zhang, WM., 2011. Solitary solutions and singular periodic solutions of the Drinfeld-Sokolov-Wilson equation by variational approach, Applied Mathematical Sciences, 5(38):1887-1894.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 1, 2019 |
| Published in Issue | Year 2019 Volume: 9 Issue: 2 |