| 1. |
- Mohammadi, Fatemeh, et al.
(författare)
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A polynomial formulation of adaptive strong stability preserving multistep methods
- 2019
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429. ; 57:1, s. 27-43
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Tidskriftsartikel (refereegranskat)abstract
- A new formulation of explicit multistep methods allows variable step-sizes by construction. This formulation can be used to construct time-adaptive strong stability preserving (SSP) multistep methods of any order for the solution of time-dependent PDEs. The new formulation is implemented in a MATLAB package, and some numerical examples are presented.
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| 2. |
- Mohammadi, Fatemeh, et al.
(författare)
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Restarting algorithms for simulation problems with discontinuities
- 2014
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Ingår i: Linköping Electronic Conference Proceedings. - : Linköping University Electronic Press. - 9789175193809 ; , s. 819-826
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Konferensbidrag (refereegranskat)abstract
- Modelica has in its language support for describing discontinuities; so-called events. Modern integrating environments; like Assimulo; provide elaborated event detection and event handling methods. In addition; the overall performance of a simulation of models with discontinuities (hybrid models) depends strongly on methods for restarting integration after event detection. The presented paper reviews two restarting methods; based oRunge--Kutta starters for multistep methods; and presents first experiments on a hybrid system described in Modelica and simulated by JModelica.org/PyFMI and Assimulo.
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| 3. |
- Mohammadi, Fatemeh, et al.
(författare)
-
Runge-Kutta Restarters for Multistep Methods in Presence of Frequent Discontinuities
- 2017
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427. ; 316, s. 287-297
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Tidskriftsartikel (refereegranskat)abstract
- Differential equations with discontinuities or differential equations coupled to discrete systems require frequent re-initializations of the numerical solution process. The classical starting process of multistep methods, based on increasing the order in the initialization phase, is computationally expensive when frequent discontinuities occur. Instead we propose to use the stage values or weight vectors of these specially constructed explicit Runge–Kutta methods for starting processes. Two practical examples demonstrate these methods.
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