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Research Article

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

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Pages 37-55 | Received 31 Mar 2023, Accepted 27 Dec 2023, Published online: 02 Feb 2024
 

Abstract

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.

MATHEMATICS SUBJECT CLASSIFICATIONS:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [No.12171177], National Natural Science Foundations of Henan Province [Nos. 222300420585, 232300420117], PhD Start-up Project of ZZULI [No. 2021BSJJ037].

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