Summary
The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
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Bader, G., Deuflhard, P. A semi-implicit mid-point rule for stiff systems of ordinary differential equations. Numer. Math. 41, 373–398 (1983). https://doi.org/10.1007/BF01418331
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DOI: https://doi.org/10.1007/BF01418331