Stiff computation
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Frequency evaluation in exponential fitting multistep algorithms for ODEs
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Explicit Time-Stepping for Stiff ODEs
SIAM Journal on Scientific Computing
On the stability of exponential fitting BDF algorithms
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Eulerian-Lagrangian time-stepping methods for convection-dominated problems
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Explicit finite difference schemes adapted to advection-reaction equations
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Smoothing schemes for reaction-diffusion systems with nonsmooth data
Journal of Computational and Applied Mathematics
On the numerical solution of the heat conduction equations subject to nonlocal conditions
Applied Numerical Mathematics
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We present BDF-type formulas capable of the exact integration (with only round-off errors) of differential equations, the solutions of which belong to the space generated by the linear combinations of «1, eAx, xeAx». Plots of their 0-stability regions in terms of λ are provided. We will see that the explicit method is 0-stable with many parameters λh. Plots of their regions' absolute stability that include all the negative real axis are provided. Numerical examples show the efficiency of the proposed codes, specially when we are integrating stiff problems with the explicit method.