A-stable Two Derivative Mono-Implicit Runge-Kutta Methods for ODEs

Author:

Aihie I. B.1,Okuonghae R. I.1

Affiliation:

1. Department of Mathematics, University of Benin, Nigeria

Abstract

An A-stable Two Derivative Mono Implicit Runge-Kutta (ATDMIRK) method is considered herein for the numerical solution of initial value problems (IVPs) in ordinary differential equation (ODEs). The methods are of high-order A-stable for $p=q=\lbrace 2s+1\rbrace _{s=2}^{7}\ $ The $p$, $q$ and $s$ are the order of the input, output and the stages of the methods respectively. The numerical results affirm the superior accuracy of the newly develop methods compare to the existing ones.

Publisher

Earthline Publishers

Reference44 articles.

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2. Abdi, A., & Hojjati, G. (2011). An extension of general linear methods. Numerical Algorithms, 57, 149-167. https://doi.org/10.1007/s11075-010-9420-y

3. Abdi, A., & Hojjati, G. (2015). Higher order second derivative methods with Runge-Kutta stability for the numerical solution of stiff ODES. Iranian Journal of Numerical Analysis and Optimization, 5(2), 1-10.

4. Aiguobasimwin, I. B., & Okuonghae, R. I. (2019). A class of two-derivative two-step Runge-Kutta methods for non-stiff ODEs. Journal of Applied Mathematics, 2019, Article ID 2459809. https://doi.org/10.1155/2019/2459809

5. Aihie, I. B., & Okuonghae, R. I. (2022). Extended Mono-Implicit Runge-Kutta methods for stiff ODEs. Journal of the Nigerian Association of Mathematics and Physics (J.NAMP), 64, 53-58.

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