Approximating resolvents for volterra integral equations


The vector-valued integral equation x(t) = a(t)-R t 0 C(t, s)x(s)ds has the variation of parameters solution x(t) = a(t) - R t 0 R(t, s)a(s)ds, where R(t, s) is the resolvent corresponding to the kernel C(t, s). We obtain insight into the behavior of R using the first-order approximant R1(t, s) = C(t, s)-R t s C(t, u)C(u, s)du, illustrating this approach with several examples. Copyright © 2013 Watam Press.

Publication Title

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

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