The mass transfer research in complex porous media and pipelines by spectral methods

2017;
: pp. 187-196
https://doi.org/10.23939/mmc2017.02.187
Received: December 22, 2017
1
Centre of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
2
Centre for Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine
3
Centre of Mathematical Modelling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine

The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper.  The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied.  The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials.  The comparative analysis for the different values of parameters is performed.  The impact of the methods parameters, in particular the partial sum order, the bit grid and the calculation error on the accuracy of the solution obtained is studied.  The calculation results are presented in the form of the tables.  The algorithm of the process of the gas motion in the pipelines using fractional derivatives is constructed.

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Math. Model. Comput. Vol.4, No.2, pp.187-196 (2017)