Second-Derivative Two-Step Mono-Implicit Runge-Kutta 
Method for Stiff ODEs

Imuwahen B. Aihie; Robert I. Okuonghae

doi:https://doi.org/10.14445/22315373/IJMTT-V70I3P101

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 70 | Issue 3 | Year 2024 | Article Id. IJMTT-V70I3P101 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I3P101

Second-Derivative Two-Step Mono-Implicit Runge-Kutta Method for Stiff ODEs

Imuwahen B. Aihie, Robert I. Okuonghae

Received	Revised	Accepted	Published
11 Jan 2024	23 Feb 2024	12 Mar 2024	30 Mar 2024

Abstract

The study explores a specific class of Second Derivative Two-step mono-implicit Runge-Kutta (SDTSMIRKs) methods within a fixed step-size environment. This method is implemented as one step method in high dimension, addressing the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The p and q denote the order of the input and output methods respectively. Numerical results from linear and non-linear stiff systems demonstrate that the newly proposed methods surpass certain existing methods in the literature.

Keywords

Second-Derivative Two-step Runge-Kutta, Order condition, A−stability, A(α)− stability, stiff IVPs.

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Citation :

Imuwahen B. Aihie, Robert I. Okuonghae, "Second-Derivative Two-Step Mono-Implicit Runge-Kutta Method for Stiff ODEs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 3, pp. 1-12, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I3P101