Geodesic
Parallel algorithms for the numerical decision of Caushy's problem for ordinary differential equations systems
Matematičeskoe modelirovanie, Tome 18 (2006) no. 9, pp. 17-31.

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In this paper the review of parallel algorithms for the decision of ordinary differential equations systems is realized. The calculable schemes of methods reflection on parallel SIMD and MIMD computing structures with different topologies: ring, matrix/tore, hypercube are developed. The comparative descriptions of potential and real parallelism are got, the numerical experiments on the system of tests are conducted. 
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L. P. Feldman; I. A. Nazarova. Parallel algorithms for the numerical decision of Caushy's  problem for ordinary differential equations systems. Matematičeskoe modelirovanie, Tome 18 (2006) no. 9, pp. 17-31. http://geodesic.mathdoc.fr/item/MM_2006_18_9_a1/

[1] Voevodin V. V., Voevodin Vl. V., Parallelnye vychisleniya, BKhV-Peterburg, SPb., 2002

[2] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR

[3] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[4] Kumar V., Gupta A., “Analyzing scalability of parallel algorithms and architectures”, Journal of Parallel and Distributed Computing., 22:3 (1994), 379–391 | DOI

[5] Golub Dzh., Van Loun Ch., Matrichnye vychisleniya, Mir, M., 1999

[6] Feldman L. P., “Parallelnye algoritmy modelirovaniya dinamicheskikh sistem, opisyvaemykh obyknovennymi differentsialnymi uravneniyami”, Elektronnoe modelirovanie, 26:1 (2004), 19–30

[7] Feldman L. P., Dmitrieva O. A., Gerber S., “Abbildung der blockartigen Algorithmen auf Parallelrechner-architekture”, Tagungsband 15. ASIM-Symposium Simulationstechnik, SCS-Europe BVBA, Ghent/Belgium 2002 (Rostock, September 2002), eds. Tavangarian D., Grutzner R., 359–364

[8] Feldman L.P., “Implementierung und Effizienzanalyse von parallelen blockartigen Simulationsalgorithmen fur dynamische Systeme mit konzentrierten Parametern”, Tagungsband 14. ASIM-Symposium Simulationstechnik, SCS-Europe BVBA, Ghent/Belgium 2000 (Hamburg, September, 2000), ed. Moller D. P. F., 241–246

[9] Feldman L. P., “Parallelnye interpolyatsionnye algoritmy chislennogo resheniya zadachi Koshi dlya obyknovennykh differentsialnykh uravnenii na SIMD kompyutere”, Nauk. tr. DonDTU. Seriya: Problemi modelyuvannya i avtomatizatsii proektuvannya dinamichnikh sistem, 10, Donetsk, 2000, 15–22

[10] Feldman L. P., Nazarova I. A., “Primenenie tekhnologii lokalnoi ekstrapolyatsii dlya vysokotochnogo resheniya zadachi Koshi na SIMD-strukturakh”, Nauchnye trudy Donetskogo natsionalnogo tekhnicheskogo universiteta. Seriya: Informatika, kibernetika i vychislitelnaya tekhnika" (IKVT-2003), 70, DonNTU, Donetsk, 2003, 98–107

[11] Nazarova I. A., Feldman L. P., “Masshtabiruemyi parallelnyi algoritm chislennogo resheniya lineinykh SODU dlya kompyuterov s raspredelennoi pamyatyu”, Tezisy dokladov V Mezhdunarodnoi konferentsii po neravnovesnym protsessam v soplakh i struyakh (NPNJ-2004) (Samara, 5–10 iyulya 2004 g.), Vuzovskaya kniga, M., 2004, 153–155

[12] Nazarova I. A., Feldman L. P., “Effektivnost parallelnogo chislennogo resheniya nezhestkikh sistem obyknovennykh differentsialnykh uravnenii s kontrolem lokalnoi pogreshnosti”, Tezisy dokladov XX Mezhdunarodnogo seminara po struinym, otryvnym i nestatsionarnym techeniyam (Sankt-Peterburg, 1–3 iyulya 2004 g.), IPTs SPbGUTD, SPb., 2004, 201–202

[13] Nazarova I. A., “Effektivnost chislennogo resheniya nezhestkikh SODU s kontrolem lokalnoi pogreshnosti dlya kompyuterov s raspredelennoi pamyatyu”, Iskusstvennyi intellekt 3'2004, Donetsk, 2004, 212–216

[14] Nazarova I. A., “Parallelnye polnostyu neyavnye metody chislennogo resheniya zhestkikh zadach dlya SODU”, Iskusstvennyi intellekt 3'2005, Donetsk, 2005, 185–193

[15] Nazarova I. A., Feldman L. P., “Razrabotka i analiz effektivnosti parallelnykh algoritmov iteratsionnykh metodov chislennogo resheniya SODU dlya multiprotsessorov s raspredelennoi pamyatyu”, Tezisy dokladov XIV Mezhdunarodnoi konferentsii po vychislitelnoi mekhanike i sovremennym prikladnym programmnym sredstvam, Vuzovskaya nauka, M., 2005, 343–345