Registered Data

[CT076]

[02343] Construction and analysis of splitting methods for Chemical Langevin Equations

  • Session Date & Time : 3D (Aug.23, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Consider modeling the stochastic dynamics underlying different chemical systems, which is usually described by the Gillespie Stochastic Simulation Algorithm (SSA), i.e. the Markov process arising from taking into account every single chemical reaction event. While exact and easy to implement, this algorithm is computationally expensive for chemical reactions involving a large number of molecular species. As an approximation, Chemical Langevin Equations (CLEs) can work for large number of species or/and reactions. In this talk, we construct an explicit splitting method applied to the system of CLEs for a simple example of a reversible bimolecular reaction. The drift term of this stochastic differential equation system satisfies a local one-sided Lipschitz condition and the diffusion term involves square root terms. We then present the main ideas of a mean-square convergence proof, as well as numerical illustrations. The results are joint work with Youssra Souli, Johannes Kepler University, Linz.
  • Classification : 60H10, 65C30, 60H35
  • Author(s) :
    • Evelyn Buckwar (Johannes Kepler University)
    • Youssra Souli (Johannes Kepler University)

[02547] Split S-ROCK methods for stiff It\^{o} stochastic differential equations

  • Session Date & Time : 3D (Aug.23, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We propose explicit stochastic Runge--Kutta methods for stiff It\^{o} stochastic differential equations. The family of the methods is constructed on the basis of the Runge--Kutta--Chebyshev methods, and we utilize a Strang splitting-type approach. The derived methods achieve weak order $2$, and have high computational accuracy for relatively large time-step size, as well as good stability properties. In numerical experiments, we confirm that our methods are superior to existing methods in computational accuracy.
  • Classification : 60H10, 65L05, 65L06
  • Author(s) :
    • Yoshio Komori (Kyushu Institute of Technology)
    • David Cohen (Chalmers University of Technology)
    • Kevin Burrage (Queensland University of Technology)

[01044] Nonlinear SPDE models of particle systems

  • Session Date & Time : 3D (Aug.23, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : Interacting particle systems provide flexible and powerful models that are useful in many application areas. However, particle systems with large numbers of particles are very complex. Therefore, a common strategy is to derive effective equations that describe the time evolution of the empirical particle density. Our aim is to consider non-Gaussian models that provide approximation of the Dean-Kawasaki equation. This is the joint work with Kremp and Perkowski.
  • Classification : 60H15, 35Q83, 65M08
  • Author(s) :
    • Ana Djurdjevac (Freie Universität Berlin)

[01806] Well-posedness of a class of SPDE with fully monotone coefficients perturbed by Levy noise

  • Session Date & Time : 3D (Aug.23, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : In this talk, we consider a class of stochastic partial differential equations with fully locally monotone coefficients in a Gelfand triplet. Under certain generic assumptions of the coefficients, we prove the existence of a probabilistic weak solution as well as the pathwise uniqueness of the solution, which implies the existence of a unique probabilistic strong solution. Finally, we allow both the diffusion and jump noise coefficients to depend on the gradient of the solution.
  • Classification : 60H15, 35R60, 35Q35
  • Author(s) :
    • Ankit Kumar (Indian Institute of Technology, Roorkee, Uttarakhand )
    • Manil T. Mohan (Indian Institute of Technology, Roorkee, Uttarakhand)

[00562] Steady-state density preserving method for second-order stochastic differential equations

  • Session Date & Time : 3D (Aug.23, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We devise a method for the long-time integration of a class of damped second-order stochastic mechanical systems. The introduced numerical scheme has the advantage of being completely explicit for general nonlinear systems while, in contrast with other commonly used integrators, it has the ability to compute the evolution of the system with high stability and precision in very large time intervals. Notably, the method has the important property of preserving, for all values of the stepsize, the steady-state probability density function of any linear system with a stationary distribution. Numerical experiments are presented to illustrate the practical performance of the introduced method.
  • Classification : 60Hxx, 65Cxx, stochastic differential equations
  • Author(s) :
    • Hugo Alexander de la Cruz Cancino (School of Applied Mathematics. FGV-EMAp)
    • Hugo de la Cruz (School of Applied Mathematics)