A convergence analysis is presented for the implicit Euler and Lie splitting schemes when applied to nonlinear parabolic equations with delay. More precisely, we consider a vector ﬁeld which is the sum of an unbounded dissipative operator and a delay term, where both point delays and distributed delays ﬁt into the framework. Such equations are frequently encountered, e.g. in population dynamics. The main theoretical result is that both schemes converge with an order (of at least) q = 1/2, without any artiﬁcial regularity assumptions. We discuss implementation details for the methods, and the convergence results are veriﬁed by numerical experiments demonstrating both the correct order, as well as the efﬁciency gain of Lie splitting as compared to the implicit Euler scheme.
The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)
- Nonlinear parabolic equations
- delay differential equations
- Convergence orders
- Implicit Euler
- Lie splitting