Abstract
Finite difference and finite element approximations for solving numerically the systems of partial differential equations, by which comprehensive models for studying complex environmental problems are studied, are proposed and discussed in this paper. First, we establish a minimum principle for the differential problem and then nonnegativity of the semidiscrete solutions. Algorithms of explicit-implicit and fully explicit schemes are realized for solution of the discrete systems. Numerical experiments are provided to illustrate the efficiency of the algorithms.
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Acknowledgements
The first, third and fourth authors are supported by the Bulgarian National Fund of Science under Projects DN 12/5-2017 and DN 12/4-2017, and the second author - by the Bilateral Project DNTS/Russia 02/12 from 2018.
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Dimov, I., Kandilarov, J., Todorov, V., Vulkov, L. (2019). Numerical Analysis of a Pollution and Environment Interaction Model. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science(), vol 11189. Springer, Cham. https://doi.org/10.1007/978-3-030-10692-8_43
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DOI: https://doi.org/10.1007/978-3-030-10692-8_43
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