[1] Mitchison G J. A model for vein formation in higher plants. Proc R Soc Lond B, 1980, 207:79-109 [2] Bell J, Cosner C, Bertiger W. Solutions for a flux-dependent diffusion model. SIAM J Math Anal, 1982, 13:758-769 [3] Roussel C J, Roussel M R. Reaction-diffusion models of development with state-dependent chemical diffusion coefficients. Prog Biophys Mol Biol, 2004, 86:113-160 [4] Dzhangveladze T A. Averaged model of sum approximation for a system of nonlinear partial differential equations (Russian). Tbiliss Gos Univ Inst Prikl Mat Trudy (Proc I Vekua Inst Appl Math), 1987, 19:60-73 [5] Dzhangveladze T A, Tagvarelia T G, Convergence of a difference scheme for a system of nonlinear partial differential equations, that arise in biology (Russian). Tbiliss Gos Univ Inst Prikl Mat Trudy (Proc I Vekua Inst Appl Math), 1990, 40:77-83 [6] Jangveladze T A. The difference scheme of the type of variable directions for one system of nonlinear partial differential equations. Proc I Vekua Inst Appl Math, 1992, 42:45-66 [7] Jangveladze T, Nikolishvili M, Tabatadze B. On one nonlinear two-dimensional diffusion system. Proc 15th WSEAS Int Conf Applied Math (MATH 10), 2010:105-108 [8] 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, 8:1550057, 21 pages [9] Kiguradze Z, Nikolishvili M, Tabatadze B. Numerical resolution of one system of nonlinear partial differential equations. Rep Enlarged Sess Semin I Vekua Appl Math, 2011, 25:76-79 [10] Douglas J. On the numerical integration of uxx + uyy=ut by implicit methods. J Soc Industr Appl Math, 1955, 3:42-65 [11] Douglas J, Peaceman D W. Numerical solution of two-dimensional heat flow problems. Amer Inst Chem Engin J, 1955, 1:505-512 [12] Peaceman D W, Rachford H H. The numerical solution of parabolic and elliptic differential equations. J Soc Industr Appl Math, 1955, 3:28-41 [13] Janenko N N. The Method of Fractional Steps for Multi-dimensional Problems of Mathematical Physics (Russian). Moscow:Nauka, 1967 [14] Marchuk G I. The Splitting-up Methods (Russian). Moscow:Nauka, 1988 [15] Samarskii A A. The Theory of Difference Schemes (Russian). Moscow, 1977 [16] Abrashin V N. A variant of the method of variable directions for the solution of multi-dimensional problems in mathematical physics. I (Russian) Differ Uravn, 1990, 26:314-323; English translation:Differ Equ, 1990, 26:243-250 |