An approximation of the analytic solution of the shock wave equation

Fathi M Allan; Kamel Al-Khaled

doi:10.1016/j.cam.2005.05.009

An approximation of the analytic solution of the shock wave equation

Fathi M Allan^*, Kamel Al-Khaled

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t < ∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.

Original language	English
Pages (from-to)	301-309
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	192
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2005.05.009
Publication status	Published - Aug 1 2006
Externally published	Yes

Keywords

Conservation law
Shock wave equations
Soliton solutions
The Adomian decomposition method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2005.05.009

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abstract = "In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t < ∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.",

keywords = "Conservation law, Shock wave equations, Soliton solutions, The Adomian decomposition method",

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AU - Al-Khaled, Kamel

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AB - In this article we discuss the analytic solution of the fully developed shock waves. The Adomian decomposition method is used to solve the shock wave equation which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 {less-than or slanted equal to} t < ∞. Also, the results presented here indicate that the method is reliable, accurate and converges very rapidly.

KW - Conservation law

KW - Shock wave equations

KW - Soliton solutions

KW - The Adomian decomposition method

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JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

An approximation of the analytic solution of the shock wave equation

Abstract

Keywords

ASJC Scopus subject areas

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