Operator splitting for nonautonomous delay equations

Abstract

We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated on some typical numerical examples.Comment: to appear in "Computers & Mathematics with Applications (CAMWA)

Implicit Euler and Lie splitting discretizations of nonlinear parabolic equations with delay

“…Finally, a general survey of other approaches and numerical methods for DDEs can be found in [5] and the references therein. See also [3,12].…”

Magnus-type integrator for semilinear delay equations with an application to epidemic models

“…We note that (e (T 2 ,T 1 ) ) T 1 ≤T 2 is an evolution family possessing the following properties (see e.g. in [4,5]):…”

“…We define a time step τ > 0 and the time levels t n = nτ for all n ∈ N 0 . Then formulae (4), (5), and (6) with T = t n and ∆T = τ lead to the following form of the Magnus method: y(t n+1 ) = e [1] (tn+τ ,0) y 0 = e [1] (tn+τ ,tn) e [1] (tn,0) y 0 = e [1] (tn+τ ,tn) y(t n ) = exp ( ∫ τ…”

Operator splitting for dissipative delay equations

“…Hence, we can integrate the first split equation explicitly, reducing the problem to solving the second equation, a classical partial differential equation. For a different splitting procedure, designed specifically for distributed delays, we refer to Csomós and Nickel [11] and Bátkai et al [1].…”