Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0991.65008
Chertock, Alina; Levy, Doron
Particle methods for dispersive equations. (English)
[J] J. Comput. Phys. 171, No.2, 708-730 (2001). ISSN 0021-9991

Summary: We introduce a new dispersion-velocity particle method for approximating solutions of linear and nonlinear dispersive equations. This is the first time in which particle methods are being used for solving such equations. Our method is based on an extension of the diffusion-velocity method of {\it P. Degond} and {\it F.-J. Mustieles} [SIAM J. Sci. Stat. Comput. 11, No. 2, 293-310 (1990; Zbl 0713.65090)] to the dispersive framework. The main analytical result we provide is the short time existence and uniqueness of a solution to the resulting dispersion-velocity transport equation. We numerically test our new method for a variety of linear and nonlinear problems. In particular, we are interested in nonlinear equations which generate structures that have nonsmooth fronts. Our simulations show that this particle method is capable of capturing the nonlinear regime of a compacton-compacton type interaction.

MSC 2000:: *65C35 Stochastic particle methods
65Z05 Applications to physics
35Q35 Other equations arising in fluid mechanics
35K55 Nonlinear parabolic equations
76R50 Diffusion

Keywords: compacton equations; parabolic equations; dispersion-velocity particle method; nonlinear dispersive equations; diffusion-velocity method; transport equation; compacton-compacton type interaction

Citations: Zbl 0713.65090

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]