The maximum principle and nonlinear monotone schemes for parabolic equations

Computational Mathematics and Mathematical Physics

Volumn 39, Issue 4, 1999, Pages 590-600

  Akimenko, V V ^a  

^a VOLODYMYR DAHL EAST UKRAINIAN NATIONAL UNIVERSITY   (Ukraine)

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[No Author keywords available]

Indexed keywords

EID: 6344274826     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (10)

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2. Samarskii, A.A., Teoriya raznostnykh skhem (The Theory of Difference Schemes), Moscow: Nauka, 1989.
3. Samarskii, A.A., On the Regularization of Difference Schemes, Zh. Vychisl. Mat. Mat. Fiz., 1967, vol. 7, no. 1, pp. 62-93.
4. Godunov, S.K., Zabrodin, A.V., Ivanov, M.Ya., et al, Chislennye melody resheniya tnnogomemykh zadach gazovoi dinamiki (Numerical Methods for Multidimensional Problems in Gas Dynamics), Moscow: Nauka, 1976.
5. Fedorenko, R.P., Application of High-Order Accurate Difference Schemes for the Numerical Solution of Hyperbolic Equations, Zh. Vychisl. Mat. Mat. Fiz., 1962, vol. 2, no. 6, pp. 1122-1128.
6. Van Leer, B., Towards the Ultimate Conservative Difference Scheme: 2. Monotonicity and Conservation Combined in a Second-Order Scheme, J. Comput. Phys., 1974, vol. 14, pp. 360-370.
7. Dymnikov, V.P. and Aloyan, A.E., Monotone Schemes for Transport Equations in Weather Prediction, Ecology, and Climate Theory, Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana, 1990, vol. 26, no. 12, pp. 1237-1247.
8. Pinchukov, V.l., Monotonization of a Family of Implicit Schemes, Zh. Vychisl. Mat. Mat. Fiz., 1990, vol. 30, no. 5, pp. 672-679.
9. Vyaznikov, K.V., Tishkin, V.F., and Favorskii, A.P., Construction of Monotone Difference Schemes on Nonuniform Grids, Mat. Model, 1989, vol. 1, no. 5, pp. 95-120.
10. D'yakonov, E.G., Difference Schemes with a Splitting Operator for Multidimensional Nonstationary Problems, Zh. Vychisl. Mat. Mat. Fiz., 1962, vol. 2, no. 4, pp. 540-568.