𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Quintic B-spline collocation method for numerical solution of the Kuramoto–Sivashinsky equation

✍ Scribed by R.C. Mittal; Geeta Arora

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
738 KB
Volume
15
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, the quintic B-spline collocation scheme is implemented to find numerical solution of the Kuramoto-Sivashinsky equation. The scheme is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The accuracy of the proposed method is demonstrated by four test problems. The numerical results are found to be in good agreement with the exact solutions. Results are also shown graphically and are compared with results given in the literature.

📜 SIMILAR VOLUMES

Numerical solutions of the generalized K
Numerical solutions of the generalized Kuramoto–Sivashinsky equation by Chebyshev spectral collocation methods
✍ A.H. Khater; R.S. Temsah 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 419 KB

Chebyshev spectral collocation methods (known as El-Gendi method [S.E. El-Gendi, Chebyshev solution of differential integral and integro-differential equations, Comput. J. 12 (1969) 282-287; B. Mihaila, I. Mihaila, Numerical approximation using Chebyshev polynomial expansions: El-gendi's method revi

Taylor–Galerkin and Taylor-collocation m
Taylor–Galerkin and Taylor-collocation methods for the numerical solutions of Burgers’ equation using B-splines
✍ İdris Dağ; Aynur Canıvar; Ali Şahin 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 559 KB

In this paper, for the numerical solution of Burgers' equation, we give two B-spline finite element algorithms which involve a collocation method with cubic B-splines and a Galerkin method with quadratic B-splines. In time discretization of the equation, Taylor series expansion is used. In order to

A collocation method with cubic B-spline
A collocation method with cubic B-splines for solving the MRLW equation
✍ A.K. Khalifa; K.R. Raslan; H.M. Alzubaidi 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 209 KB

The modified regularized long wave (MRLW) equation is solved numerically by collocation method using cubic B-splines finite element. A linear stability analysis of the scheme is shown to be marginally stable. Three invariants of motion are evaluated to determine the conservation properties of the al