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Noori Y. Abdul-Hassan, Zainab J. Kadum and Ali Hasan Ali
In this paper, we propose a new numerical scheme based on a variation of the standard formulation of the Runge?Kutta method using Taylor series expansion for solving initial value problems (IVPs) in ordinary differential equations. Analytically, the accu...
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Zacharoula Kalogiratou and Theodoros Monovasilis
Two-Derivative Runge?Kutta methods have been proposed by Chan and Tsai in 2010 and order conditions up to the fifth order are given. In this work, for the first time, we derive order conditions for order six. Simplifying assumptions that reduce the numbe...
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Jens Lang and Bernhard A. Schmitt
This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We combine the property of superconvergence of some standar...
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