Stiff computation
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
SIAM Journal on Scientific Computing
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Block-Boundary Value Methods for the Solution of Ordinary Differential Equations
SIAM Journal on Scientific Computing
Solving Index-1 DAEs in MATLAB and Simulink
SIAM Review
Evaluation of a Test Set for Stiff ODE Solvers
ACM Transactions on Mathematical Software (TOMS)
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Nonstandard finite difference method by nonlocal approximation
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Adaptive stiff solvers at low accuracy and complexity
Journal of Computational and Applied Mathematics - Special issue: The international conference on computational methods in sciences and engineering 2004
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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 @d0 (where @d0 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 afterwards becomes non-stiff again. We provide its asymptotic and numerical solution obtained via a variety of methods. Comparisons are made for the numerical results which we obtain with the MATLAB ode solvers (ode45, ode15s and ode23s) and some nonstandard finite difference methods. Results corresponding to standard finite difference method are also presented. Furthermore, the discussion on these approaches along with the others, provides several open problems for new and young researchers.