Explicit Stabilized Multirate Method For Stiff Differential Equations
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The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupl ...
In this thesis we investigate different ways of approximating the solution of the chemical master equation (CME). The CME is a system of differential equations that models the stochastic transient behaviour of biochemical reaction networks. It does so by d ...
Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to ...
In this report we study and compare particular integration methods to solve ordinary differential equations, which are separable in solvable parts. The main source for this work is the article of Blanes and Casas: "On the necessity of negative coefficient ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standar ...
Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...
Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving with time. A particular application arises in the modeling of atmospheric particles. Discontinuity poi ...
A novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated ...
Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computat ...