MATHEMATICAL MODELING OF DIFFUSION BOUNDARY PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS USING MATLAB AND C++ FOR NUMERICAL AND ANALYTICAL SOLUTIONS

Authors

  • Edmunds Lukaševičs Rēzeknes Tehnoloģiju akadēmija
  • Ilmārs Kangro Zinātniska darba vadītājs, Mg.math., Dr.paed.,Rēzeknes Tehnoloģiju akadēmija

DOI:

https://doi.org/10.17770/het2023.27.7373

Keywords:

3-D initial boundary value problem, periodic boundary conditions, (1D) non-stationary and stationary boundary proble, heavy metal Ca, peat layer, Matlab, C .,

Abstract

The article examines a second-order parabolic partial differential equation of a three-dimensional (3D) non-stationary boundary problem with constant diffusion coefficients and periodic boundary conditions in the x and y directions. The method for reducing the (3D) non-stationary boundary problem to the corresponding one-dimensional (1D) non-stationary boundary problem using periodic boundary conditions in the x and y directions is discussed. The stationary (analytical) solution of the obtained (1D) stationary boundary problem is also obtained. The numerical solutions of the 1D boundary problem are obtained using the Matlab package "pdepe" and the C++ programming language. As a practical application of the developed mathematical model, the article discusses calculating the concentration of heavy metal Ca in a peat layer based on the obtained experimental data (measurements).

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References

Kangro I., Kalis H., Gedroics A., Teirumnieka E., Teirumnieks E. On mathematical

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Orru, H., Orru, M. 2006. Sources and distribution of trace elements in Estonian

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De la Rosa, G., Peralta-Videa, J.R., Gardea-Torresdey, J.L. 2003. Utilization of ICP/OES for the determination of trace metal binding to different humid fractions. Journal of Hazardous Materials, B97, pp. 207-218.

Kalis H., Kangro I. Effective finite difference and Conservative Averaging methods for solving problems of mathematical physics. Monography. Rezekne Academy of Technologies, 2021, 423p. http:books.rta.lv/index.php/RTA/catalog/book/24

C++, vector class. https://learn.microsoft.com/en-gb/cpp/standard-library/vector-class?view=msvc-170

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Published

2023-10-30