𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the approximation of solutions of the generalized Korteweg–de Vries–Burger's equation

✍ Scribed by Ohannes Karakashian; William McKinney

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
726 KB
Volume
37
Category
Article
ISSN
0378-4754

No coin nor oath required. For personal study only.

✦ Synopsis

We propose numerical schemes for approximating periodic solutions of the generalized Korteweg-de Vries-Burgers equation. These schemes are based on a Galerkin-finite element formulation for the spatial discretization and use implicit Runge-Kutta (IRK) methods for time stepping. Asymptotically optimal rate of convergence estimates can be obtained in terms of the spatial and temporal discretization parameters.

In particular, the temporal rates are the classical ones, i.e. no order reduction occurs. We also apply Newton's method, to solve the system of nonlinear equations. Indeed, Newton's method yields iterants that converge quadratically and preserves the optimal rates of convergence.

📜 SIMILAR VOLUMES

The generalized Korteweg–de Vries–Burger
The generalized Korteweg–de Vries–Burgers equation in
✍ Tomasz Dlotko 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 292 KB

The generalized KdV-Burgers equation u t +(δu xx +g(u)) x -νu xx +γ u = f (x), δ, ν > 0, γ ≥ 0, is considered in this paper. Using the parabolic regularization technique we prove local and global solvability in H 2 (R) of the Cauchy problem for this equation. Several regularity properties of the app

Septic B-spline method of the Korteweg-d
Septic B-spline method of the Korteweg-de Vries–Burger’s equation
✍ Talaat S. Aly El-Danaf 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 201 KB

In this paper, a numerical solution for the Korteweg-de Vries-Burger's equation (KdVB) by using the collocation method using the septic splines is proposed. Applying the Von-Neumann stability analysis technique we show that the method is unconditionally stable. By conducting a comparison between the