High order explicit exponential Runge-Kutta methods for semilinear delay differential equations
High order explicit exponential Runge-Kutta methods for semilinear delay differential equations
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DOI：
10.1016/j.cam.2020.113279
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Jinwei Fang;Rui Zhan
中科院分区：
文献类型：
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作者：
Jinwei Fang;Rui Zhan
本文旨在分析刚性半线性时滞微分方程高阶显式指数龙格-库塔方法的阶次条件。在解析半群的框架和时滞微分方程的自然假设下，推导了高达五阶的刚性阶条件。此外，我们证明即使 p 阶的阶数条件保持弱形式，该方法也是 p 阶的刚性收敛。进行数值测试以证明高阶方法的优越性。
This paper aims to analyze order conditions of high order explicit exponential Runge–Kutta methods for stiff semilinear delay differential equations. Under the framework of analytic semigroup and the natural assumptions on the delay differential equations, the stiff order conditions up to order five are derived. Further, we show the method is stiffly convergent of order p even if the order conditions of order p holding in a weak form. Numerical tests are carried out to demonstrate the superiority of high order methods.