Convergence of osculatory quadrature formulae

Donaldson, J. D.

doi:10.1007/bf01932397

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2024

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“…Recently, [5] presented an Extended Mono-Implicit Runge-kutta (EMIRK) method for solving ordinary differential equations (ODEs) which is build upon the existing Mono-implicit Runge-Kutta (MIRK) methods in [ [8], [26], [9], [19], [25], [20]]. The general format of the method discussed in [5] is…”

Section: Introductionmentioning

confidence: 99%

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

Aihie,

Okuonghae

2024

EJMS

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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.

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