A first order method is considered for the discretization in time of an integro-differential equation, which can be written as Dα u(t) = A u(t) + f(t), 1 < α < 2, where A : D(A) ⊂ X → X is a sectorial operator in a Banach space X. Qualitative properties of the numerical solution, such as contractivity and positivity, are studied. A numerical illustration is provided.
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Cuesta et al. (2003) studied this question.
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