Geodesic
Example of automatic code generation of numerical modeling application for solution of the Fokker--Planck equation
Matematičeskoe modelirovanie, Tome 27 (2015) no. 9, pp. 49-64.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper focuses on accelerating the application development cycle of numerical simulation using automatic code generation system — Symbalg, based on the concept of skeletons for different classes of problems. As an example, the system is used for the solution of the Fokker–Planck equation using the method of stochastic analog. The paper presents the simulation results for nonlinear Brownian motion and uniaxial ion ferroelectric. Also the paper presents the examples of calculations to study stochastic resonance.
Mots-clés : Fokker–Planck equation, uniaxial ion ferroelectric, Symbalg
Keywords: stochastic resonance, code generation. 
@article{MM_2015_27_9_a3,
     author = {S. A. Zhdanov and A. V. Ivanov},
     title = {Example of automatic code generation of numerical modeling application for solution of the {Fokker--Planck} equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {49--64},
     publisher = {mathdoc},
     volume = {27},
     number = {9},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_9_a3/}
}
TY  - JOUR
AU  - S. A. Zhdanov
AU  - A. V. Ivanov
TI  - Example of automatic code generation of numerical modeling application for solution of the Fokker--Planck equation
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 49
EP  - 64
VL  - 27
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_9_a3/
LA  - ru
ID  - MM_2015_27_9_a3
ER  - 
%0 Journal Article
%A S. A. Zhdanov
%A A. V. Ivanov
%T Example of automatic code generation of numerical modeling application for solution of the Fokker--Planck equation
%J Matematičeskoe modelirovanie
%D 2015
%P 49-64
%V 27
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2015_27_9_a3/
%G ru
%F MM_2015_27_9_a3
S. A. Zhdanov; A. V. Ivanov. Example of automatic code generation of numerical modeling application for solution of the Fokker--Planck equation. Matematičeskoe modelirovanie, Tome 27 (2015) no. 9, pp. 49-64. http://geodesic.mathdoc.fr/item/MM_2015_27_9_a3/

[1] B. Buchberger, G. Collins, R. Loos, Computer algebra — symbolic and algebraic computation, Springer, New York, 1983, 410 pp. | MR

[2] J. Davenport, Y. Siret, E. Tournier, Computer algebra: systems and algorithms for algebraic computation, Academic Press Ltd., London, 1988, 267 pp. | MR

[3] G. Rossum, F. L. Dzh. Dreik, D. S. Otkidach, Iazyk programmirovaniia Python, 2001, 454 pp.

[4] M. Lutz, Learning Python, 4th Edition, O'Reilly Media, 2009, 1216 pp.

[5] R. A. Suzi, Iazyk programmirovaniia Python, INTUIT, BINOM, Laboratoriia znanii, M., 2006, 328 pp.

[6] B. Stroustrup, The C++ Programming Language, Fourth Edition, Addison Wesley, Reading, Mass. USA, 2013, 1360 pp.

[7] D. J. Higham, N. J. Higham, MATLAB Guide, 2nd edition, SIAM, Philadelphia, 2005 | MR | Zbl

[8] D. V. Kirianov, Samouchitel Mathcad 13, BVKH-Peterburg, 2006

[9] D. Barthou, O. Brand-Foissac, O. Pene, G. Grosdidier, R. Dolbeau et al., “Automated Code Generation for Lattice Quantum Chromodynamics and beyond”, Journal of Physics: Conference Series, Institute of Physics: Open Access Journals, 510 (2014), 012005

[10] Yu. L. Klimontovich, Statistical Theory of Open Systems, Springer Netherlands, 1995, 569 pp.

[11] G. I. Zmievskaia, “Chislennye stohasticheskie modeli neravnovesnyh protsessov”, Matem. modelirovanie, 8:11 (1996), 3–40 | MR

[12] Yu. L. Klimontovich, What are stochastic filtering and stochastic resonance?, Phys. Usp., 42:1 (1999), 37–44 | MR

[13] P. S. Landa, Yu. I. Neimark, P. V. E. McClintock, “Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise”, Journal of Statistical Physics, 125:3 (2006), 593–620 | MR

[14] A. V. Ivanov, S. A. Khilkov, S. A. Zhdanov, Biblioteka aivlib

[15] M. M. Gorbunov-Posadov, Rasshiriaemye programmy, Poliptikh, M., 1999, 336 pp.

[16] V. D. Levchenko, “Asinkhronnye parallelnye algoritmy kak sposob dostizheniia effektivnosti vychislenii”, Informatsionnye tekhnologii i vychislitelnye sistemy, 2005, no. 1

[17] G. E. Uhlenbeck, G. W. Ford, Lectures in Statistical Mechanics, American Mathematical Society, Providence, 1963 | MR | Zbl

[18] V. I. Zubov, “Nesimmetrizovannye funktsii raspredeleniia I samosoglasovannaia teoriia silno angarmonicheskikh kristallov”, Vestnik RUDN, seriia Fizika, 2003, no. 11, 119–141

[19] Make, https://www.gnu.org/software/make/

[20] Simplified Wrapper and Interface Generator, http://www.swig.org/

[21] S. M. Ermakov, Metod Monte-Karlo i smezhnye voprosy, Nauka, M., 1975, 472 pp. | MR