Two-step Runge–Kutta methods for Volterra integro-differential equations

被引：0
作者：
Wen J. [1 ]
Huang C. [2 ,3 ]
Guan H. [1 ]
机构：
[1] College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou
[2] School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan
[3] Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan
来源：
International Journal of Computer Mathematics | 2024年 / 101卷 / 01期
基金：
中国国家自然科学基金;
关键词：
convergence; stability; two-step Runge–Kutta methods; Volterra integro-differential equation;
D O I：
10.1080/00207160.2023.2301555
中图分类号：
学科分类号：
摘要：
In this paper, we investigate two-step Runge–Kutta methods to solve Volterra integro-differential equations. Two-step Runge–Kutta methods increase the order of convergence in comparing the classical Runge–Kutta method without extra computational cost. First, the local order conditions and convergence theorem are derived. Then, stability properties of two-step Runge–Kutta methods corresponding to the basic and convolution test equations are analysed. Furthermore, one-stage method with order four and two-stage method with order six are constructed and we plot the stability regions. Numerical examples are presented to confirm the theoretical analyses. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
引用
收藏
页码：37 / 55
页数：18
相关论文
共 35 条
[1]  
Abdi A., Hosseini S.A., The barycentric rational difference-quadrature scheme for systems of Volterra integro-differential equations, SIAM J. Sci. Comput., 40, pp. A1936-A1960, (2018)
[2]  
Baker C.T., Makroglou A., Short E., Regions of stability in the numerical treatment of Volterra integro-differential equations, SIAM J. Numer. Anal., 16, pp. 890-910, (1979)
[3]  
Bakke V., Jackiewicz Z., Stability of numerical methods for Volterra integro-differential equations of convolution type, ZAMM Z. Angew. Math. Mech., 68, pp. 89-100, (1988)
[4]  
Bartoszewski Z., Jackiewicz Z., Construction of two-step Runge–Kutta methods of high order for ordinary differential equations, Numer. Algorithms, 18, pp. 51-70, (1998)
[5]  
Bellen A., Jackiewicz Z., Vermiglio R., Zennaro M., Stability analysis of Runge–Kutta methods for Volterra integral equations of the second kind, IMA J. Numer. Anal., 10, pp. 103-118, (1990)
[6]  
Brunner H., On the numerical solution of nonlinear Volterra integro-differential equations, Nordisk Tidskr. Informationsbehandling (BIT), 13, pp. 381-390, (1973)
[7]  
Brunner H., Implicit Runge–Kutta methods of optimal order for Volterra integro-differential equations, Math. Comp., 42, pp. 95-109, (1984)
[8]  
Brunner H., Collocation Methods for Volterra Integral and Related Functional Differential Equations, (2004)
[9]  
Brunner H., Lambert J., Stability of numerical methods for Volterra integro-differential equations, Computing, 12, pp. 75-89, (1974)
[10]  
Brunner H., Norsett S.P., Wolkenfelt P.H.M.
1234