A Numerical Method for an Integro-Differential Equation with Memory in Banach Spaces: Qualitative Properties

Authors:
E. Cuesta;C. Palencia
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2003

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Abstract

A first order method is considered for the discretization in time of an integro-differential equation, which can be written as $D^{\alpha} u(t) = A u(t) + f(t)$, $1 X. Qualitative properties of the numerical solution, such as contractivity and positivity, are studied. A numerical illustration is provided.