Explicit difference schemes for solving stiff problems with a complex or separable spectrum

Computational Mathematics and Mathematical Physics

Volumn 40, Issue 12, 2000, Pages 1729-1740

  Lebedev, V I ^a  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042643160     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. Lebedev, V.I., Explicit Difference Schemes with Variable Time Steps for Stiff Systems of Equations, Preprint of Inst. Numerical Mathematics, USSR Acad. Sci., Moscow, 1987, no. 177.
2. Lebedev, V.I., How to Solve Stiff Systems of Equations by Explicit Difference Schemes, Vychislitel'nye protsessy i sistemy (Computational Processes and Systems), Moscow: Nauka, 1991, pp. 237-291.
3. Lebedev, V.I., Explicit Difference Schemes with Time-Variable Steps for Solution of Stiff Systems of Equations, Sov. J. Numer. Anal. Math. Model., 1989, vol. 4, no. 2, pp. 111-135.
4. Lebedev, V.I., How to Solve Stiff Systems of Equations by Explicit Difference Schemes, Numerical Methods and Applications, Boca Raton: CRC, 1994, pp. 45-80.
5. Lebedev, V.I., Explicit Difference Schemes with Variable Time Steps for Solving Stiff Systems of Equations, Lect. Notes Comput. Sci., 1196. Numer. Anal. Appl., Springer-Verlag, 1997, pp. 274-283.
6. Lebedev, V.I., Explicit Difference Schemes for Solving Stiff Systems of ODEs and PDEs with Complex Spectrum, Russ. J. Numer. Math. Math. Model., 1998, vol. 5, no. 2, pp. 107-116.
7. Lebedev, V.I. and Medovikov, A.A., A Second-Order Accurate Explicit Method for Solving Stiff Systems of Ordinary Differential Equations, Izv. Vyssh. Uchebn. Zaved., Mat., 1998, no. 9 (436), pp. 55-63.
8. Medovikov, A.A., High-Order Explicit Methods for Parabolic Equations, BIT, 1998, vol. 38, no. 2, pp. 372-390.
9. Medovikov, A.A., Third-Order Explicit Method for the Stiff Ordinary Differential Equations, Lect. Notes in Comput. Sci., 1196. Numer. Anal. Appl., Springer-Verlag, 1997, pp. 327-334.
10. Lebedev, V.I. and Finogenov, S.A., On the Use of Ordered Chebyshev Parameters in Iterative Methods, Zh. Vychisl. Mat. Mat. Fiz., 1976, vol. 16, no. 4, pp. 895-907.
11. Lebedev, V.I., An Introduction to Functional Analysis and Computational Mathematics, Boston: Birkhäuser, 1996.
12. Hairer, E. and Wanner, G., Solving Ordinary Differential Equations: Stiff and Differential-Algebraic Problems, Berlin: Springer-Verlag, 1996, 2nd rev. ed. Translated under the title Reshenie obyknovennykh differentsial'nykh uravnenii: Zhestkie i differentsial'no-algebraicheskie zadachi, Moscow: Mir, 1999.
13. Fedorenko, R.P., Stiff Systems of Ordinary Differential Equations and Their Numerical Integration, Vychislitel'nye protsessy i sistemy (Computational Processes and Systems), Moscow: Nauka, 1991, pp. 328-380.
14. Dement'ev, V.G., Lebedev, V.I., and Nechepurenko, Yu.M., Spectral Analysis of a Reactor Model with Delayed Neutrons, Algoritmy i progranmy dlya neitronno-fizicheskikh raschetov yadernykh reaktorov (Algorithms and Computer Programs for Reactor Neutron Dynamics Computations), Obninsk: Neitronika-98, 1999, pp. 143-150.
15. Bakhvalov, N.S., Zhidkov, N.P., and Kobel'kov, G.M., Chislennye metody (Numerical Methods), Moscow: Nauka, 1987.
16. Lebedev, V.I., The Equations and Convergence of a Differential Difference Method (the Method of Lines), Vestn. Mosk. Gos. Univ., 1955, no. 10, pp. 47-57.
17. Lebedev, V.I., Loutsenko, S.V., and Lycossov, V.N., Large-Eddy Simulation of Convective Boundary Layer Using Explicit Difference Schemes, Russ. J. Numer. Math. Math. Model., 2000, vol. 15, no. 1, pp. 95-110.