Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third-Order IVPs

Pertanika Journal of Science and Technology(2023)

引用 0|浏览3
暂无评分
摘要
This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u^''' (t)=f(t,u(t),u^' (t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions e^ѡt and e^(-ѡt)for exponentially fitted and e^iѡt and e^(-iѡt) for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution.
更多
查看译文
关键词
frequency-dependent,two-derivative,runge-kutta,third-order
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要