论文标题
用于延迟的进化方程的二阶Magnus型积分器
A second-order Magnus-type integrator for evolution equations with delay
论文作者
论文摘要
我们将抽象延迟方程重写为非自主抽象的库奇问题，使我们能够为前者引入Magnus型积分器。我们证明获得的Magnus型积分器的二阶收敛性。我们还表明，如果涉及的差分运算符承认其生成的半群的常见集合，那么Magnus型积分器也将尊重这个不变的集合，从而使假设较弱以获得所需的收敛。作为一个说明性的例子，我们考虑了一个具有潜在时期和扩散的空间依赖性流行模型。
We rewrite abstract delay equations to nonautonomous abstract Cauchy problems allowing us to introduce a Magnus-type integrator for the former. We prove the second-order convergence of the obtained Magnus-type integrator. We also show that if the differential operators involved admit a common invariant set for their generated semigroups, then the Magnus-type integrator will respect this invariant set as well, allowing for much weaker assumptions to obtain the desired convergence. As an illustrative example we consider a space-dependent epidemic model with latent period and diffusion.
