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In this paper, we present various new algorithms for the integration of stiff differential equations that allow the step size to increase proportionally with time. We mainly focus on high precision integrators, which leads us to use high order Taylor schemes. We will also present various algorithms for certifying the numerical results, again with the property that the step size increases with time.
Keywords: stiff differential equation, numerical method, reliable computation, rigorous integration, Taylor models, multiple precision computations
A.M.S. subject classification: 65L04, 65L20, 65G20, 37-04