PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Method of lines for parabolic stochastic functional partial differential equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We approximate parabolic stochastic functional differential equations substituting the derivatives in the space variable by finite differences. We prove the stability of the method of lines corresponding to a parabolic SPDE driven by Brownian motion.
Rocznik
Strony
443--456
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
  • University of Gdansk Institute of Mathematics Wit Stwosz Street 57, 80-952 Gdansk
Bibliografia
  • [1] J. Bebernes, R. Ely, Comparison Techniques and the Method of Lines for a Parabolic Functional Equation, Defense Technical Information Center, 1981.
  • [2] C.R. Doering, C. Mueller, P. Smereka, Interacting particles, the stochasatic Fisher--Kolmogorov-Petrovsky-Pisconov equation, and duality, Physica A 325 (2003), 243–259.
  • [3] S.A. Dubey, The method of lines applied to nonlinear nonlocal functional differential equations., J. Math. Anal. Appl. 376 (2011) 1, 275–281.
  • [4] K. Elworthy, H. Zhao, J. Gaines, The propagation of travelling waves for stochastic generalized KPP equations, Mathematical and Computer Modelling, 20 (4–5), (1994), 131–166.
  • [5] R. Fisher, The wave of advance of advantageous genes, Ann. Eugenics, 7 (1937), 353–369.
  • [6] A. Friedman, Stochastic differential equations and applications, number v. 1 [in:] Probability and Mathematical Statistics, Academic Press, 1975.
  • [7] I. Gyöngy, Lattice approximations for stochastic Quasi-Linear parabolic partial differential equations driven by Space-Time white noise i, Potential Anal. 9 (1998) 1, 1–25.
  • [8] I. Gyöngy, D. Nualart, Implicit scheme for quasi-linear parabolic partial differential equations driven by space-time white noise, Potential Anal. 7 (1997), 725–757.
  • [9] J. Hale, S. Lunel, Introduction to Functional Differential Equations, vol. 99 [in:] Applied Mathematical Sciences, Springer, 1993.
  • [10] S. Hamdi, W. H. Enright, Y. Ouellet, W. E. Schiesser, Method of lines solutions of the extended Boussinesq equations, J. Comput. Appl. Math. 183 (2005) 2, 327–342.
  • [11] S. Haq, N. Bibi, S.I.A. Tirmizi, M. Usman, Meshless method of lines for the numerical solution of generalized kuramoto-sivashinsky equation, Appl. Math. Comput. 217 (2010) 6, 2404–2413.
  • [12] S. Haq, A. Hussain, M. Uddin, On the numerical solution of nonlinear Burgers’-type equations using meshless method of lines, Appl. Math. Comput. 218 (2012) 11, 6280–6290.
  • [13] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Mathematics and Its Applications, Kluwer Academic Publishers, 1999.
  • [14] J. Kauthen, The Method of Lines for Parabolic Partial Integro-differential Equations, Publications internes de la Section de mathématiques de l’Université de Genève, Université de Genève-Section de mathématiques, 1989.
  • [15] A. Kolmogorov, I. Petrovskii, N. Piscunov, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Byul. Moskovskogo Gos. Univ. 1, (1937) 6, 1–25.
  • [16] T. Koto, Method of lines approximations of delay differential equations, Comput. Math. Appl. 48 (2004) 1–2, 45–59.
  • [17] C. Kuehn, Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts, Theoretical Ecology 6 (2013), 295–308.
  • [18] H. Leszczynski, Comparison ODE theorems related to the method of lines, J. Appl. Anal. 17 (2011), 137–154.
  • [19] C.-Y. Lin, The method of lines for solving a class of abstract differential equations, Nonlinear Anal. TMA 45 (2001), 383–390.
  • [20] G.J. Lord, T. Shardlow, Postprocessing for stochastic parabolic partial differential equations, SIAM J. Numerical Analysis 45 (2007) 2, 870–889.
  • [21] S.C. Reddy, L.N. Trefethen, Stability of the method of lines, Numer. Math. 62 (1992), 235–267.
  • [22] A. Rößler, M. Seaïd, M. Zahri, Method of lines for stochastic boundary-value problems with additive noise, Appl. Math. Comput. 199 (2008) 1, 301–314.
  • [23] J. Seidler, Ergodic behaviour of stochastic parabolic equations, Czechoslovak Math. J. 47 (1997) 277–316.
  • [24] J. Walsh, Finite element methods for parabolic stochastic PDE’s, Potential Anal. 23 (2005) 1, 1–43.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a7fe1567-0796-4f77-94e9-6f14da8c01c8
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.