Search Results - "Kloeden, P. E."

The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds by Kloeden, P.E., Lord, G.J., Neuenkirch, A., Shardlow, T.

“…We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a…”
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The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus by Kloeden, P. E., Shardlow, T.

“…The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has…”
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Dynamics of a class of ODEs more general than almost periodic by Kloeden, P.E., Rodrigues, H.M.

“…A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when…”
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Stable Integration of Stiff Random Ordinary Differential Equations by Asai, Y., Herrmann, E., Kloeden, P. E.

“…Implicit one-step numerical schemes are presented for the pathwise simulation of stiff random ordinary differential equations (RODEs), specifically an implicit…”
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Attractors of set-valued partial differential equations under discretization by Kloeden, P. E., Valero, J.

“…The approximation of the global attractor of a dissipative set-valued reaction–diffusion equation is investigated when a Galerkin approximation is used to…”
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Mathematical Consistency and Long-Term Behaviour of a Dynamical System with a Self-Organising Vector Field by Janson, N. B., Kloeden, P. E.

“…A dynamical system with a plastic self-organising velocity vector field was introduced in Janson and Marsden (Sci Rep 7:17007, 2017) as a mathematical…”
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Random attractors for stochastic semi-linear degenerate parabolic equations by Yang, Meihua, Kloeden, P.E.

“…The existence of a random attractor is established for a class of stochastic semi-linear degenerate parabolic equations with the leading term of the form div (…”
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Pullback attractors of a multi-valued process generated by parabolic differential equations with unbounded delays by Wang, Yejuan, Kloeden, P.E.

“…The theory of nonautonomous multi-valued dynamical systems and a method of asymptotic compactness based on the concept of the Kuratowski measure of the…”
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Multi-step methods for random ODEs driven by Itô diffusions by Asai, Y., Kloeden, P.E.

“…Linear multi-step methods are derived for random ordinary differential equations (RODEs) driven by the solutions of Itô stochastic differential equations…”
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Numerical schemes for random ODEs with affine noise by Asai, Y., Kloeden, P. E.

“…Numerical schemes for random ordinary differential equations, abbreviated RODEs, with an affine structure can be derived in a similar way as for affine control…”
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Nonautonomous bifurcation scenarios in SIR models by Kloeden, P. E., Pötzsche, C.

“…The standard obstacles in developing a bifurcation theory for nonautonomous differential equations are the lack of steady‐state equilibria and the…”
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On the asymptotical behavior of nonautonomous dynamical systems by Yejuan, Wang, Desheng, Li, Kloeden, P.E.

“…The uniform asymptotical behavior of nonautonomous dynamical systems and their attractors is investigated. In particular, it is shown that parametrically…”
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Weak pullback attractors of setvalued processes by Caraballo, T., Kloeden, P.E., Marı́n-Rubio, P.

“…Weak pullback attractors are defined for nonautonomous setvalued processes and their existence and upper semicontinuous convergence under perturbation is…”
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Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients by Jentzen, A., Kloeden, P. E., Neuenkirch, A.

“…We study the approximation of stochastic differential equations on domains. For this, we introduce modified Itô–Taylor schemes, which preserve approximately…”
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Higher order numerical schemes for affinely controlled nonlinear systems by GRÜNE, L, KLOEDEN, P. E

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Asymptotic behaviour of nonlocal reaction–diffusion equations by Anguiano, M., Kloeden, P.E., Lorenz, T.

“…The existence of a global attractor in L 2 ( Ω ) is established for a reaction–diffusion equation on a bounded domain Ω in R d with Dirichlet boundary…”
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Synchronization of Discrete Time Dynamical Systems by Kloeden, P.E.

“…The synchronization of two discrete time dynamical systems is considered, where the systems are described in terms of first order difference equations, each of…”
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Nonautonomous attractors of switching systems by Kloeden, P. E.

“…Switching systems formed by switching between a finite number of autonomous ordinary differential equations are formulated as abstract nonautonomous dynamical…”
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Higher-order implicit strong numerical schemes for stochastic differential equations by KLOEDEN, P. E, PLATEN, E

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Runge-Kutta methods for monotone differential and delay equations by KLOEDEN, P. E, SCHROPP, J

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