ERENA: A fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics
2016
Abstract We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. 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. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
Keywords:
- Mathematical optimization
- Mathematics
- Exponential integrator
- Mathematical analysis
- Explicit and implicit methods
- Runge–Kutta methods
- Collocation method
- Method of lines
- Backward differentiation formula
- Numerical methods for ordinary differential equations
- Numerical partial differential equations
- Differential algebraic equation
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