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Zastosowanie metod numerycznego odwrócenia przekształcenia Laplace’a w modelowaniu matematycznym wybranych procesów inżynierii chemicznej

Wójcik M.

Technical Issues

2015

nr 3

56--62

The main aim of this work was a choice of a suitable numerical inversion method of Laplace transform to solving the model of gas flow through the measuring system for the determination of effective diffusion coefficient. In this paper, selected numerical Laplace inversion methods have been shown. These methods were implemented in the computer algebra system Maple®. Calculations have been made for a few tests of mathematical functions and the equation of heat conduction. The results allowed us to compare the accuracy of the calculations and speed of selected numerical inversion methods for Laplace transform. The Gaver-Stehfest method has proven the most effective to solving this problem.

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.

The Application of the Laplace Transform for Modeling of Gas Flow Using Maple®

Wójcik M., Szukiewicz M., Kowalik P.

Journal of Applied Computer Science Methods

2014

Vol. 6 No. 1

43--53

The Laplace transform is powerful method for solving differential equations. This paper presents the application of Laplace transform to solve the mathematical model of gas flow through the measuring system. The basis of the mathematical model used to describe and simulate the analyzed process is a system of ordinary differential equations. As a result is obtained a single algebraic equation in terms of the complex variable s. In order to study the dynamics of the system these equation should be reverted to the time domain by performing an inverse Laplace transform. Calculations were performed in the environment of Maple®. Determining of mixing in a u-shape vessel is aim of presented calculations.