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2 2015

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Application of Numerical Laplace Inversion Methods in Chemical Engineering with Maple®

Wójcik M., Szukiewicz M., Kowalik P.

Journal of Applied Computer Science Methods

2015

Vol. 7 No. 1

5--15

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 GaverStehfest 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 GaverStehfest method has proven the most effective. The model was developed using the computer algebra system Maple®. Implementation of the methods were done by authors.

Mathematical modelling of dynamic processes in gas transmission

Prytula N.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2015

Vol. 4, No 3

57--63

The problem of finding the parameters of the gas transmission system in terms of its operations under unsteady operating modes are considered. We show mathematical models of gas flows in the basic facilities in the system with a complicated piping diagram. The solution is built to solve a system of partial differentia equations with the finite element method of large dimension with boundary conditions, some of which are designed in the process of solving the system of equations. This is due to the provision of technical and technological constraints on the pressure of the controlled points of the system. On the resistance to finding a solution significantly affects a step of the time coordinate. The proposed algorithm in the editing process of flow diagrams provides an increase in stability of solving systems of equations, and significantly reduces the time for the simulation.