A stability analysis of the trapezoidal method for Volterra integral equations with completely positive kernels

AbstractThe 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