Conservative numerical method for a system of semilinear singularly perturbed parabolic reaction‐diffusion equations

References

• Brainina , Kh.Z. and Neyman , E.Ya. 1982 . Hardphase reactions in electroanalytical chemistry , Moskva : Khimia . (in Russian)
   Google Scholar
• Friedman , A. 1964 . Partial differential equations of parabolic type. , Englewood Cliffs, N.J. : Prentice‐Hall, Inc .
   Google Scholar
• Grigoriev , V.A. and Zorin , V.M. , eds. 1982 . Heat engineering experiment: Handbook , Moskva : Energoizdat . (in Russian)
   Google Scholar
• Il'in , A.M. 1992 . Matching of Asymptotic Expansions of Solutions of Boundary Value Problems. , Vol. 102 , USA : Americal Mathematical Society . Translations of Mathematical Monographs
   Google Scholar
• Ladyzhenskaya , O.A. , Solonnikov , V.A. and Ural'tseva , N.N. 1968 . Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs , Vol. 23 , USA : Americal Mathematical Society .
   Google Scholar
• O'Riordan , E. and Shishkin , G.I. 2008 . Parameter uniform numerical methods for singularly perturbed elliptic problems with parabolic boundary layers . Appl. Num. Math., , 58 (12) : 1761 – 1772 .
   Web of Science ®Google Scholar
• Paskonov , V.M. , Polejaev , V.I. and Chudov , L.A. 1984 . Numerical modeling of heat and mass transfer processes , Moskva : Nauka . (in Russian)
   Google Scholar
• Samarskii , A.A. 2001 . The Theory of Difference Schemes. , New York : Marcel Dekker .
   Google Scholar
• Shishkin , G.I. 1992 . Discrete approximation of singularly perturbed elliptic and parabolic equations. , Ekaterinburg : Russian Academy of Sciences, Ural Section . (in Russian)
   Google Scholar
• Shishkin , G.I. 1995 . Grid approximation of singularly perturbed boundary value problems for systems of elliptic and parabolic equations . Comp. Maths. Math. Phys., , 35 (4) : 1155 – 1171 .
   Web of Science ®Google Scholar
• Shishkin , G.I. 1998 . Grid approximation of singularly perturbed systems of elliptic and parabolic equations with convective terms . Differential Equations, , 34 (12) : 1693 – 1704 .
   Web of Science ®Google Scholar
• Shishkin , G.I. 2006 . Grid approximation of singularly perturbed parabolic convection‐diffusion equations subject to a piecewise smooth initial condition . Comp. Maths. Math. Phys., , 46 (1) : 49 – 72 .
   Google Scholar
• Shishkin , G.I. 2007 . Approximation of systems of elliptic reaction‐diffusion equations with two perturbation parameters . Comp. Maths. Math. Phys., , 47 (5) : 797 – 828 .
   Google Scholar
• Shishkin , G.I. and Shishkina , L.P . 2008 . Approximation of a system of semilinear singularly perturbed parabolic reaction‐diffusion equations on a vertical strip . Journal of Physics: Conference Series, , (accepted)
   PubMedGoogle Scholar
• Shishkin , G.I. and Shishkina , L.P . 2008 . Approximation of a system of singularly perturbed parabolic equations in a rectangle . Comp. Maths. Math. Phys., , 48 (4) : 627 – 640 .
   Web of Science ®Google Scholar
• Shishkin , G.I. and Shishkina , L.P . 2009 . Difference Methods for Singular Perturbation Problems , Monographs & Surveys in Pure & Applied Math. Chapman and Hall/CRC .
   Google Scholar
• Shishkina , L.P and Shishkin , G.I. 2008 . Robust numerical method for a system of singularly perturbed parabolic reaction‐diffusion equations on a rectangle . Math. Model. Anal., , 13 (2) : 251 – 261 . (doi:10.3846/1392–6292.2008.13.251–261)
   Web of Science ®Google Scholar
• This research was supported by the Russian Foundation for Basic Research under grants Nos. 07–01–00729, by the Boole Centre for Research in Informatics at the National University of Ireland in Cork, and by the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland mathematics initiative grant 06/MI/005.
   Google Scholar