Abstract
An explicit multistep one-stage method is considered, which allows numerical integration of the differential equations that constitute the basis of the atmosphere circulation model by transforming the initial–boundary-value convection–diffusion problem to the Cauchy problem. The method has an advantage over the available methods due to its high precision and low computational cost.
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V. A. Prusov and A. Yu. Doroshenko, Modeling of Natural and Technogenic Processes in the Atmosphere [in Russian], Naukova Dumka, Kyiv (2006).
S. K. Godunov and V. S. Ryaben’kii, Difference Schemes (An Introduction to the Theory) [in Russian], Nauka, Moscow (1973).
P. J. Roache, Fundamentals of Computational Fluid Dynamics, Hermosa Pub., Albuquerque (1998).
A. A. Samarskii and E. S. Nikolaev, Methods to Solve Finite-Difference Equations [in Russian], Nauka, Moscow (1978).
V. P. Sadokov (ed.), Numerical Methods used in Atmospheric Models [in Russian], Gidrometeoizdat, Leningrad (1982).
P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, J. Wiley & Sons, New York–London (1962).
H. J. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations, Springer, Berlin–Heidelberg–New York (1973).
A. Yu. Doroshenko and V. A. Prusov, “Methods of efficient modeling and forecasting regional atmospheric processes,” in: I. Faragó, Á. Havasi, and K. Georgiev (eds.), Advances in Air Pollution Modeling for Environmental Security, NATO Science Series, 54, Springer-Verlag (2005), pp. 143–152.
V. A. Prusov, A. E. Doroshenko, and R. I. Chernysh, “A method for numerical solution of a multidimentional convection–diffusion problem,” Cybern. Syst. Analysis, 45, No. 1, 89–95 (2009).
V. A. Prusov, A. E. Doroshenko, and R. I. Chernysh, “Choosing the parameter of a modified additive-averaged splitting algorithm,” Cybern. Syst. Analysis, 45, No. 4, 589–596 (2009).
V. A. Prusov, A. E. Doroshenko, R. I. Chernysh, and L. N. Guk, “Efficient difference scheme for numerical solution of a convective diffusion problem,” Cybern. Syst. Analysis, 43, No. 3, 368–376 (2007).
V. Prusov, A. Doroshenko, I. Faragó, and Á. Havasi, “On the numerical solution of the three-dimensional advection-diffusion equation,” Probl. Programmir., No. 2–3, 641–647 (2006).
V. A. Prusov and A. Yu. Doroshenko, “On efficient numerical solution of one-dimensional convection–diffusion equations in modeling atmospheric processes,” Intern. J. of Environment and Pollution, 32, No. 2, 231–249 (2008).
D. Anderson, J. C. Tannehill, and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer, Hemisphere, New York (1984).
E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II. Stiff and Differential–Algebraic Problems, Springer Series in Comput. Mathematics, Vol. 14, Springer-Verlag (1991).
L. M. Skvortsov, “Explicit multistep method for the numerical solution of stiff differential equations,” Comput. Math. Math. Physics, 47, No. 6, 915–923 (2007).
A. A. Samarskii and P. N. Vabishchevich, Numerical Methods to Solve Convection–Diffusion Problems [in Russian], Editorial URSS (1999).
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2015, pp. 62–70.
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Prusov, V.A., Doroshenko, A.Y. Multistep Method of the Numerical Solution of the Problem of Modeling the Circulation of Atmosphere in the Cauchy Problem. Cybern Syst Anal 51, 547–555 (2015). https://doi.org/10.1007/s10559-015-9745-6
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DOI: https://doi.org/10.1007/s10559-015-9745-6