We consider the combustion equation as one of the candidates from the class of stiff ordinary differential equations. A solution over a length of time that is inversely proportional to δ > 0 (where δ > 0 is a small disturbance of the pre-ignition state) is sought. This problem has a transient at the midpoint of the integration interval. The solution changes from being non-stiff to stiff, and af...

The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic. rate equations is presented, Different integration methods are tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, homogeneous gasPhase combustion reactions. It is shown that selective use of no...

It is well known that the numerical solution of stochastic ordinary differential equations leads to a step size reduction when explicit methods are used. This has led to a plethora of implicit methods with a wide variety of stability properties. However, for stochastic problems whose eigenvalues lie near the negative real axis, explicit methods with extended stability regions can be very effect...

For reaction–diffusion–advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction–diffusion systems with both stiff reaction and diffusi...