Geodesic
Development and testing for methods of solving stiff ordinary differential equations
Matematičeskoe modelirovanie i čislennye metody, no. 4 (2014), pp. 95-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is aimed at research of the (m,k)-method, CROS, finite superelement method and 4-stage explicit Runge–Kutta method for solving stiff systems of ordinary differential equations. Analysis of tests results showed that the best choice for systems with high stiffness is CROS. The finite superelement method is the «precise» method for solving linear systems of ordinary differential equations, the best supporting method for its implementation is (4,2)-method. The variation of the finite superelement method has been built and tested for solving nonlinear problems, this method proved to be unsuitable for problems with high stiffness.
Keywords: The paper is aimed at research of the (m,k)-method, cros, finite superelement method and 4-stage explicit runge–kutta method for solving stiff systems of ordinary differential equations. analysis of tests results showed that the best choice for systems with high stiffness is cros. the finite superelement method is the «precise» method for solving linear systems of ordinary differential equations, the best supporting method for its implementation is (4,2)-method. the variation of the finite superelement method has been built and tested for solving nonlinear problems, this method proved to be unsuitable for problems with high stiffness. 
@article{MMCM_2014_4_a6,
     author = {M. P. Galanin and S. R. Khodzhaeva},
     title = {Development and testing for methods of solving stiff ordinary differential equations},
     journal = {Matemati\v{c}eskoe modelirovanie i \v{c}islennye metody},
     pages = {95--119},
     year = {2014},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMCM_2014_4_a6/}
}
TY  - JOUR
AU  - M. P. Galanin
AU  - S. R. Khodzhaeva
TI  - Development and testing for methods of solving stiff ordinary differential equations
JO  - Matematičeskoe modelirovanie i čislennye metody
PY  - 2014
SP  - 95
EP  - 119
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MMCM_2014_4_a6/
LA  - ru
ID  - MMCM_2014_4_a6
ER  - 
%0 Journal Article
%A M. P. Galanin
%A S. R. Khodzhaeva
%T Development and testing for methods of solving stiff ordinary differential equations
%J Matematičeskoe modelirovanie i čislennye metody
%D 2014
%P 95-119
%N 4
%U http://geodesic.mathdoc.fr/item/MMCM_2014_4_a6/
%G ru
%F MMCM_2014_4_a6
M. P. Galanin; S. R. Khodzhaeva. Development and testing for methods of solving stiff ordinary differential equations. Matematičeskoe modelirovanie i čislennye metody, no. 4 (2014), pp. 95-119. http://geodesic.mathdoc.fr/item/MMCM_2014_4_a6/

[1] Galanin M.P., Savenkov E.B., Methods of numerical analysis of mathematical models, BMSTU Publ., Moscow, 2010, 591 pp.

[2] Kalitkin N.N., Numerical methods, Nauka Publ., Moscow, 1978, 512 pp. | MR

[3] Arushanyan O.B., Zaletkin S.F., Kalitkin N.N., Numerical Methods and Programming, 3 (2002), 11–19

[4] Novikov E.A., Computational Technologies, 12:5 (2007), 103–115 | Zbl

[5] Kalitkin N.N., “Semi-explicit schemes for the problems of high rigidity”, Encyclopedia of low emperature plasma, 7:1 (2008), 153–171 | MR

[6] Al’shin A.B., Al’shina E.A., Kalitkin N.N., Koryagina A.B., Computational Mathematics and Mathematical Physics, 46:8 (2006), 1392–1414 | MR

[7] Al’shin A.B., Al’shina E.A., Limonov A.G., Computational Mathematics and Mathematical Physics, 49:2 (2009), 270–287 | MR | Zbl

[8] Shirkov P.D., Mathematical Models and Computer Simulations, 4:8 (1992), 47–57 | MR | Zbl

[9] Kalitkin N.N., Panchenko S.L., Mathematical Models and Computer Simulations, 11:6 (1999), 52–81 | MR | Zbl

[10] Rosenbrock H., “Some general implicit processes for the numerical solution of differential equations.”, Comput J., 5:4 (1963), 329–330 | DOI | MR | Zbl

[11] Fedorenko R.P., An Introduction to Computational Physics, MIPT Publ., Moscow, 1994, 528 pp.

[12] Galanin M.P., Milyutin D.C., Savenkov E.B., “The development, research and application of the finite super element method for solving biharmonic equation”, Keldysh Institute of Applied Mathematics RAS, 2005, no. 59, 26 pp.

[13] Galanin M.P., Savenkov E.B., “The method of finite superelement for the problem of high-speed skin layer”, Keldysh Institute of Applied Mathematics RAS, 2004, no. 3, 32 pp.

[14] Galanin M.P., Savenkov E.B., Computational Mathematics and Mathematical Physics, 43:5 (2003), 713-729 pp. | MR | Zbl

[15] Samarsky A.A., Gulin A.V., Numerical methods., Nauka Publ., Moscow, 1989, 432 pp. | MR

[16] Hairer E., Norsett S., Wanner J., Solving ordinary differential equations. Part 2. Stiff and Differential-Algebraic Problems, Springer, New York etc., 1991 | MR | Zbl

[17] Galanin M.P., Khodzhaeva S.R., “The methods of solving stiff ordinary differential equations”, The results of test calculations. Keldysh Institute of Applied Mathematics RAS, 2013, 98, 29 pp.