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Jangveladze T, Kiguradze Z, Gagoshidze M, Nikolishvili M. Stability and convergence of the variable directions difference scheme for one nonlinear two-dimensional model. INT J BIOMATH 2015. [DOI: 10.1142/s1793524515500576] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.
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Affiliation(s)
- Temur Jangveladze
- Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University, 2 University Street, 0186 Tbilisi, Georgia
- Georgian Technical University, 77 Kostava Ave., 0175 Tbilisi, Georgia
| | - Zurab Kiguradze
- Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University, 2 University Street, 0186 Tbilisi, Georgia
| | - Mikheil Gagoshidze
- Sokhumi State University, 12 Politkovskaya Street, 0186 Tbilisi, Georgia
| | - Maia Nikolishvili
- Ivane Javakhishvili Tbilisi State University, 2 University Street, 0186 Tbilisi, Georgia
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