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In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials.
SIC can be run either in a steady-state mode, which calculates the equilibrium concentrations of the modelled components, or in a time-dependent mode where the concentrations are advanced in time using the modified Euler method for stiff equations.
Samant and Vlachos developed a multiscale Monte Carlo method for stiff systems where partial equilibrium occurs [ 23].
Isodyn implements several methods for ODE solving provided for C++ by Press et al [ 30], including fourth-order Runge-Kutta, Bulirsch-Stoer and Rosenbrock method for stiff systems.
Also is implemented implicit Runge-Kutta 5th order method for stiff systems (Radau5), described in [ 31] and backward differentiation formulas as their implemented in the solver DASSL [ 32] written in Fortran but linked with the C++ code of Isodyn.
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Thus, alternatives to the usual methods for stiff systems integration become available.
Nevertheless, these methods for stiff problems are very sensitive to the computing of the Jacobian matrix for the correction.
We develop a class of numerical methods for stiff systems, based on the method of exponential time differencing.
The underlying ideas are introduced and developed in the context of linearly implicit methods for stiff equations.
Our results show that symmetrization in both modes improves accuracy and efficiency, and can restore the classical order of the Gauss methods for stiff linear problems.
ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2.
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