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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.22 n.1 San José Jan./Jun. 2015
Special software for computing the special functions of wave catastrophes
Software especial para calcular las funciones especiales de catástrofes de olas
Software especial para calcular las funciones especiales de catástrofes de olas
Abstract
The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and inter-operability.
Keywords: ODE method; special functions of wave catastrophes; numerical methods; algorithms; parallel computing; distributed computing.
Resumen
Se considera el método de ecuaciones diferenciales ordinarias en el contexto de calcular funciones especiales de catástrofes de olas. Se describen métodos y algoritmos numéricos complementarios. El artículo muestra enfoques para acelerar tales cálculos usando capacidades modernas de sistemas de cálculo. Se consideran métodos para calcular funciones especiales de catástrofes de olas en el marco de computación en paralelo y sistemas distribuidos. El artículo cubre el proceso de desarrollo de software especial para calcular funciones especiales, así como asuntos de portabilidad, extensibilidad e interoperabilidad.
Palabras clave: métodos de EDO; funciones especiales de catástrofes de olas; métodos numéricos; algoritmos; computación en paralelo; computación distribuida.
Mathematics Subject Classication: 78A99.
Ver contenido en pdf.
References
[1] Arnold, V.I. (1992) Catastrophe Theory, 3rd edition. Springer, Berlin. [ Links ]
[2] Dorokhina, T.V.; Kryukovsky, A.S.; Malyshenko, A.B. (2008) "Development of numerical algorithms for the calculation and visualization of wave catastrophes", RosNOU Bulletin. Management, Computing and Informatics 3 Russian New University, Moscow: 25-47. [ Links ]
[3] Ipatov, E.B.; Kryukovsky, A.S.; Lukin, D.S.; Palkin, E.A. (1986)"Edge catastrophes and asymptotics", Reports of the Academy of Sciences, USSR, 291(4): 823-827. [ Links ]
[4] Kryukovsky, A.S. (1992)"Method of ordinary differential equations for computing the special functions of wave catastrophes (SWC)", Diffraction and Propagation of Electromagnetic Waves: Interagency Collection of Scientic Papers, Moscow: MIPT: 29-48. [ Links ]
[5] Kryukovsky, A.S.; Lukin, D.S.; Palkin, E.A. (1995) "Uniform asymptotics and corner catastrophes", Reports of the Russian Academy of Sciences 341(4): 456-459. [ Links ]
[6] Kryukovsky, A.S. (2013) "The uniform asymptotic theory of edge and corner wave catastrophes", Monograph, Russian New University, Moscow. [ Links ]
[7] Kryukovsky, A.S.; Lukin, D.S. (2003) "The theory of calculating the reference focal and diffraction electromagnetic fields on the basis of special functions of wave catastrophes", Technology and Electronics 48(8), Moscow (in Russian): 912-921. [ Links ]
[8] Shampine, L.F. (2005) "Error estimation and control for ODEs", Journal of Scientic Computing 25(1): 3-16. [ Links ]
[2] Dorokhina, T.V.; Kryukovsky, A.S.; Malyshenko, A.B. (2008) "Development of numerical algorithms for the calculation and visualization of wave catastrophes", RosNOU Bulletin. Management, Computing and Informatics 3 Russian New University, Moscow: 25-47. [ Links ]
[3] Ipatov, E.B.; Kryukovsky, A.S.; Lukin, D.S.; Palkin, E.A. (1986)"Edge catastrophes and asymptotics", Reports of the Academy of Sciences, USSR, 291(4): 823-827. [ Links ]
[4] Kryukovsky, A.S. (1992)"Method of ordinary differential equations for computing the special functions of wave catastrophes (SWC)", Diffraction and Propagation of Electromagnetic Waves: Interagency Collection of Scientic Papers, Moscow: MIPT: 29-48. [ Links ]
[5] Kryukovsky, A.S.; Lukin, D.S.; Palkin, E.A. (1995) "Uniform asymptotics and corner catastrophes", Reports of the Russian Academy of Sciences 341(4): 456-459. [ Links ]
[6] Kryukovsky, A.S. (2013) "The uniform asymptotic theory of edge and corner wave catastrophes", Monograph, Russian New University, Moscow. [ Links ]
[7] Kryukovsky, A.S.; Lukin, D.S. (2003) "The theory of calculating the reference focal and diffraction electromagnetic fields on the basis of special functions of wave catastrophes", Technology and Electronics 48(8), Moscow (in Russian): 912-921. [ Links ]
[8] Shampine, L.F. (2005) "Error estimation and control for ODEs", Journal of Scientic Computing 25(1): 3-16. [ Links ]
*Faculty of Information Systems and Computer Technology, Russian New University, Radio st., 22, 105005 Moscow, Russia. E-mail: kryukovsky@rambler.ru
†Moscow Institute of Physics and Technology (State University), Institutskiy lane 9, 141700 Dolgoprudny, Moscow Region, Russia. E-mail: lukin@mail.mipt.ru
‡Faculty of Information Systems and Computer Technology, Russian New University, Radio st., 22, 105005 Moscow, Russia. E-mail: rogachevsergei@gmail.com
Received: 16/Dec/2013; Revised: 3/Oct/2014;Accepted: 17/Oct/2014
