Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1172.65037
Dehghan, Mehdi; Shakeri, Fatemeh
The numerical solution of the second Painlevé equation. (English)
[J] Numer. Methods Partial Differ. Equations 25, No. 5, 1238-1259 (2009). ISSN 0749-159X; ISSN 1098-2426/e

Summary: The Painlevé equations were discovered by Painlevé, Gambier and their colleagues during studying a nonlinear seccond-order ordinary differential equation. The six equations which bear Painlevé's name are irreducible in the sense that their general solutions cannot be expressed in terms of known functions. Painlevé has derived these equations on the sole requirement that their solutions should be free from movable singularities. Many situations in mathematical physics reduce ultimately to Painlevé equations: applications including statistical mechanics, plasma physics, nonlinear waves, quantum gravity, quantum field theory, general relativity, nonlinear optics, and fiber optics. This fact has caused a significant interest to the study of these equations in recent years. In this study, the solution of the second Painlevé equation is investigated by means of Adomian decomposition method, homotopy perturbation method, and Legendre tau method. Then a numerical evaluation and comparison with the results obtained by the method of continuous analytic continuation are included.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34M55 Painlevé and other special equations
35Q53 KdV-like equations
37K10 Completely integrable systems etc.

Keywords: Adomian decomposition method; homotopy perturbation method; Kadomtsev-Petviashvili equation; Legendre tau method; modified Korteweg-de Vries equation; Painlevé equations; numerical examples

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]