Reduction of stiffness‐induced round‐off errors in chemical reaction systems

Lukassen, Axel Ariaan; Kiehl, Martin
November 2019
PAMM: Proceedings in Applied Mathematics & Mechanics;Nov2019, Vol. 19 Issue 1, pN.PAG
Academic Journal
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 source term requests subtraction of very large numbers, and round‐off errors by cancellation occur. This can cause severe convergence problems within Newton's method, resulting in step size reductions. The system of differential equations is replaced by a less stiff modified system in order to reduce the round‐off errors and the computing time. Thereby the approximation error between the given system of differential equations and the modified system of differential equations is smaller than the given tolerance.


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