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Open AccessArticle
Positive Fitted Finite Volume Method for Semilinear Parabolic Systems on Unbounded Domain
by
Miglena N. Koleva
Miglena N. Koleva 1,*
and
Lubin G. Vulkov
Lubin G. Vulkov 2,*
1
Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria
2
Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria
*
Authors to whom correspondence should be addressed.
Axioms 2024, 13(8), 507; https://doi.org/10.3390/axioms13080507 (registering DOI)
Submission received: 24 June 2024
/
Revised: 23 July 2024
/
Accepted: 25 July 2024
/
Published: 27 July 2024
Abstract
This work deals with a semilinear system of parabolic partial differential equations (PDEs) on an unbounded domain, related to environmental pollution modeling. Although we study a one-dimensional sub-model of a vertical advection–diffusion, the results can be extended in each direction for any number of spatial dimensions and different boundary conditions. The transformation of the independent variable is applied to convert the nonlinear problem into a finite interval, which can be selected in advance. We investigate the positivity of the solution of the new, degenerated parabolic system with a non-standard nonlinear right-hand side. Then, we design a fitted finite volume difference discretization in space and prove the non-negativity of the solution. The full discretization is obtained by implicit–explicit time stepping, taking into account the sign of the coefficients in the nonlinear term so as to preserve the non-negativity of the numerical solution and to avoid the iteration process. The method is realized on adaptive graded spatial meshes to attain second-order of accuracy in space. Some results from computations are presented.
Share and Cite
MDPI and ACS Style
Koleva, M.N.; Vulkov, L.G.
Positive Fitted Finite Volume Method for Semilinear Parabolic Systems on Unbounded Domain. Axioms 2024, 13, 507.
https://doi.org/10.3390/axioms13080507
AMA Style
Koleva MN, Vulkov LG.
Positive Fitted Finite Volume Method for Semilinear Parabolic Systems on Unbounded Domain. Axioms. 2024; 13(8):507.
https://doi.org/10.3390/axioms13080507
Chicago/Turabian Style
Koleva, Miglena N., and Lubin G. Vulkov.
2024. "Positive Fitted Finite Volume Method for Semilinear Parabolic Systems on Unbounded Domain" Axioms 13, no. 8: 507.
https://doi.org/10.3390/axioms13080507
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