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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:
76M25Other numerical methods (fluid mechanics)
76N15Gas dynamics, general