Asymptotic expansions and boundary conditions for time-dependent problems
SIAM Journal on Numerical Analysis
Artificial boundary conditions for the linear advection diffusion equation
Mathematics of Computation
Convolution quadrature and discretized operational calculus I.
Numerische Mathematik
Absorbing boundary conditions for diffusion equations
Numerische Mathematik
Artificial boundary conditions for diffusion equations: numerical study
Journal of Computational and Applied Mathematics
Spatial Invasion of Pine Beetles into Lodgepole Forests: A Numerical Approach
SIAM Journal on Scientific Computing
On Markov reward modelling with FSPNs
Performance Evaluation
Modelling with Generalized Stochastic Petri Nets
ACM SIGMETRICS Performance Evaluation Review - Special issue on Stochastic Petri Nets
SIAM Journal on Scientific Computing
Stochastic Petri nets: an elementary introduction
Advances in Petri Nets 1989, covers the 9th European Workshop on Applications and Theory in Petri Nets-selected papers
Discrete-event simulation of fluid stochastic Petri nets
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Open boundary conditions for a parabolic system
Mathematical and Computer Modelling: An International Journal
Applied Numerical Mathematics
Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean
SIAM Journal on Scientific Computing
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In this work we construct and analyse transparent boundary conditions (TBCs) for general systems of parabolic equations. These TBCs are constructed for the fully discrete scheme (@q-method, finite differences), in order to maintain unconditional stability of the scheme and to avoid numerical reflections. The discrete transparent boundary conditions (DTBCs) are discrete convolutions in time and are constructed using the solution of the Z-transformed exterior problem. We will analyse the numerical error of these convolution coefficients caused by the inverse Z-transformation. Since the DTBCs are non-local in time and thus very costly to evaluate, we present approximate DTBCs of a sum-of-exponentials form that allow for a fast calculation of the boundary terms. Finally, we will use our approximate DTBCs for an example of a fluid stochastic Petri net and present numerical results.