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A new approach to the gas dynamics equation: An application of the decomposition method. (English) Zbl 1017.76070

Summary: We use the Adomian decomposition method to implement the homogeneous gas dynamics equations. The analytic solution of the equations is calculated in the form of a series with easily computable components. The homogeneous problem is quickly solved by observing the self-canceling “noise” terms whose sum vanishes in the limit. The comparison of the methodology with some other known techniques shows that the present approach is effective and powerfull. Many test modeling problems from mathematical physics, both linear and nonlinear, are discussed to illustrate the effectiveness of the decomposition method.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics (general theory)
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References:

[1] Buden R. L., Numerical Analysis (1993)
[2] Smith C. D., Numerical Solution of Rirtial Differential Equations (1978)
[3] Adomian G., Solving Frontier Problems of Physics: The decomposition method (1994) · Zbl 0802.65122
[4] DOI: 10.1016/0022-247X(88)90170-9 · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[5] DOI: 10.1016/0096-3003(94)00137-S · Zbl 0826.65077 · doi:10.1016/0096-3003(94)00137-S
[6] DOI: 10.1016/0022-247X(87)90318-0 · Zbl 0624.60079 · doi:10.1016/0022-247X(87)90318-0
[7] DOI: 10.1016/0022-247X(85)90311-7 · Zbl 0575.60064 · doi:10.1016/0022-247X(85)90311-7
[8] DOI: 10.1016/S0096-3003(97)10127-8 · Zbl 0943.65084 · doi:10.1016/S0096-3003(97)10127-8
[9] Kaya D., Bulletin of the Instutite of Mathematics Academia Sinica. 28 pp 35– (2000)
[10] van Tonningen S., Comp. Educ. Journal 5 pp 30–
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