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The timescales of chemical reactions range from nanoseconds to minutes. Hence, chemical reaction systems result in stiff systems of differential equations. Usually, implicit integration schemes are used in order to solve these stiff systems of differential equations. Thus, Newton's method is used in order to solve a nonlinear equation system in each time step. Thereby the evaluation of the chemical...
Chemical reaction systems often result in high‐dimensional, stiff differential equations. Solving these differential equations is computational demanding. The computational effort can be reduced by the usage of an operator splitting scheme. The most frequently used splitting schemes are the Lie‐Trotter splitting [1] and the Strang splitting [2]. However, the usage of a splitting scheme results in...
Splitting methods are frequently used for large scale chemical reaction systems. The main reason is the reduced computational cost for solving the subproblems in comparison to the time integration of the full problem. However, a splitting error is introduced. The most popular splitting schemes are the first order Lie–Trotter splitting and the second order Strang splitting. However, in case of stiff...
We present a new method for parameter estimation for elliptic partial differential equations. Parameter estimation requires the evaluation of the partial differential equation for many different parameter sets. Therefore, model order reduction is reasonable. Model order reduction is composed of an offline phase and an online phase. In the offline phase the reduced model is constructed using snapshots...
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