Информационни системи за симулиране на поведението на горски и полски пожари

ИМИ-БАН, 04.04.2012 г., присъждане на образователна и научна степен "доктор" на Нина Христова Добринкова по научна специалност 01.01.12 информатика. [Dobrinkova Nina Hristova; Добринкова Нина Христова

Approximating the solution stochastic process of the random Cauchy one-dimensional heat model

[EN] This paper deals with the numerical solution of the random Cauchy one-dimensional heat model. We propose a random finite difference numerical scheme to construct numerical approximations to the solution stochastic process. We establish sufficient conditions in order to guarantee the consistency and stability of the proposed random numerical scheme.The theoretical results are illustrated by means of an example where reliable approximations of the mean and standard deviation to the solution stochastic process are given.This work has been partially supported by the Ministerio de Economía y Competitividad Grant MTM2013-41765-P. Ana Navarro Quiles acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València. M. A. Sohaly is also indebted to Egypt Ministry of Higher Education, Cultural Affairs, for its financial support [mohe-casem (2016)].Navarro Quiles, A.; Romero, J.; Roselló, M.; Sohaly, M. (2016). Approximating the solution stochastic process of the random Cauchy one-dimensional heat model. Abstract and Applied Analysis. 2016:1-7. https://doi.org/10.1155/2016/5391368S172016Logan, J. D. (2004). Partial Differential Equations on Bounded Domains. Undergraduate Texts in Mathematics, 121-171. doi:10.1007/978-1-4419-8879-9_4Wang, J. (1994). A Model of Competitive Stock Trading Volume. Journal of Political Economy, 102(1), 127-168. doi:10.1086/261924Tsynkov, S. V. (1998). Numerical solution of problems on unbounded domains. A review. Applied Numerical Mathematics, 27(4), 465-532. doi:10.1016/s0168-9274(98)00025-7Koleva, M. N. (2006). Numerical Solution of the Heat Equation in Unbounded Domains Using Quasi-uniform Grids. Lecture Notes in Computer Science, 509-517. doi:10.1007/11666806_58Han, H., & Huang, Z. (2002). A class of artificial boundary conditions for heat equation in unbounded domains. Computers & Mathematics with Applications, 43(6-7), 889-900. doi:10.1016/s0898-1221(01)00329-7Wu, X., & Sun, Z.-Z. (2004). Convergence of difference scheme for heat equation in unbounded domains using artificial boundary conditions. Applied Numerical Mathematics, 50(2), 261-277. doi:10.1016/j.apnum.2004.01.001Cortés, J. C., Sevilla-Peris, P., & Jódar, L. (2005). Analytic-numerical approximating processes of diffusion equation with data uncertainty. Computers & Mathematics with Applications, 49(7-8), 1255-1266. doi:10.1016/j.camwa.2004.05.015Casabán, M.-C., Cortés, J.-C., García-Mora, B., & Jódar, L. (2013). Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar. Abstract and Applied Analysis, 2013, 1-9. doi:10.1155/2013/676372Casabán, M.-C., Company, R., Cortés, J.-C., & Jódar, L. (2014). Solving the random diffusion model in an infinite medium: A mean square approach. Applied Mathematical Modelling, 38(24), 5922-5933. doi:10.1016/j.apm.2014.04.063Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Øksendal, B. (2003). Stochastic Differential Equations. Universitext. doi:10.1007/978-3-642-14394-6Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. doi:10.1007/978-3-662-12616-5Holden, H., Øksendal, B., Ubøe, J., & Zhang, T. (2010). Stochastic Partial Differential Equations. doi:10.1007/978-0-387-89488-

Approximation of reachable sets using optimal control algorithms

To appearInternational audienceNumerical experiences with a method for the approximation of reachable sets of nonlinear control systems are reported. The method is based on the formulation of suitable optimal control problems with varying objective functions, whose discretization by Euler's method lead to finite dimensional non-convex nonlinear programs. These are solved by a sequential quadratic programming method. An efficient adjoint method for gradient computation is used to reduce the computational costs. The discretization of the state space is more efficiently than by usual sequential realization of Euler's method and allows adaptive calculations or refinements. The method is illustrated for two test examples. Both examples have non-linear dynamics, the first one has a convex reachable set, whereas the second one has a non-convex reachable set