In this paper, the procedure of choice of the effective numerical inversion method of Laplace transform for solving of the mathematical model of gas flow was shown. Two inversion methods are evaluated in this work: the Gaver-Stehfest method, and the Dubner and Abate method. The numerical tests has been made using test functions. Based on the test results the fast and accurate method was selected and applied for modeling of the gas flow. The Gaver-Stehfest method has proven the most effective. The model was developed using the computer algebra system Maple?. Implementation of the methods were done by authors.
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