Monotone high-order accurate schemes for transport and parabolic equations

Computational Mathematics and Mathematical Physics

Volumn 39, Issue 5, 1999, Pages 805-816

  Akimenko, V V ^a  

^a VOLODYMYR DAHL EAST UKRAINIAN NATIONAL UNIVERSITY   (Ukraine)

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[No Author keywords available]

Indexed keywords

EID: 33747103108     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (7)

1. Akimenko, V.V., Maximum Principle and Nonlinear Monotone Schemes for Parabolic Equations, Zh. Vychisl. Mat. Mat. Fiz., 1999, vol. 39, no. 4, pp. 618-629.
2. Obukhov, A.M., On the Accuracy of Precalculation of Ad vective Variations of Fields in Numerical Weather Forecast, Izv. Akad. Nauk SSSR, Ser. Geofiz., 1957, no. 9, pp. 1133-1141.
3. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1989.
4. Godunov, S.K., A Method for Numerical Calculation of Discontinuous Solutions to Fluid-Dynamics Equations, Matem. Sb., 1959, vol. 47 (89), no. 3, pp. 271-306.
5. Fromm, J.E., A Method for Reducing in Convective Difference Schemes, IBM Res. Lab. Rep., 1968.
6. Dymnikov, V.P. and Aloyan, A.E., Monotone Schemes for Solving Transport Equations in Problems of Weather Forecast, Ecology, and Climate Theory, Izv. Akad. Nauk SSSR, Fiz. Atm. Okeana, 1990, vol. 26, no. 12, pp. 12371247.
7. Van Leer, B., Towards the Ultimate Conservative Difference Schemes II: Monotonicity and Conservation Combined in a Second-Order Scheme, J. Comput. Phys., 1974, vol. 14, pp. 360-370.