TY - JOUR
T1 - A stability analysis of the trapezoidal method for Volterra integral equations with completely positive kernels
AU - Bellen, A.
AU - Jackiewicz, Zdzislaw
AU - Vermiglio, R.
AU - Zennaro, M.
N1 - Funding Information:
* Supported by the Italian Government from M. P. I. funds (40%). + Supported by Consiglio Nazionale delle Ricerche and by the National under Grant NSF DMS-8.520900.
PY - 1990/11/1
Y1 - 1990/11/1
N2 - The solution of the Volterra integral equation with completely positive kernel y(t) + ∝0t b(t - s) y(s) ds = u0 + ∝0t b(t - s) g(s) ds, t ≥ 0, is nonnegative and nonincreasing provided that g is nonincreasing and 0 ≤ g(t) ≤ u0 for any t > 0. We prove that under some additional hypotheses this property is inherited by the solution of the recurrence relation resulting from applying the trapezoidal method to this equation.
AB - The solution of the Volterra integral equation with completely positive kernel y(t) + ∝0t b(t - s) y(s) ds = u0 + ∝0t b(t - s) g(s) ds, t ≥ 0, is nonnegative and nonincreasing provided that g is nonincreasing and 0 ≤ g(t) ≤ u0 for any t > 0. We prove that under some additional hypotheses this property is inherited by the solution of the recurrence relation resulting from applying the trapezoidal method to this equation.
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U2 - 10.1016/0022-247X(90)90068-Q
DO - 10.1016/0022-247X(90)90068-Q
M3 - Article
AN - SCOPUS:38249018314
SN - 0022-247X
VL - 152
SP - 324
EP - 342
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -