New class of hybrid explicit methods for numerical solution of optimal control problems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 Forward-backward sweep method (FBSM) is an indirect numerical method used for solving optimal control problems, in which the differential equation arising from this method is solved by the Pontryagin’s maximum principle.
M. Ebadi, I. Malih Maleki, A. Ebadian
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Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations [PDF]
International Journal of Mathematical, Engineering and Management Sciences, 2019 The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to work out on differential equation of the type’s explicit, implicit, partial and delay differential equation etc.
Vijeyata Chauhan +1 more
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Order conditions for partitioned Runge-Kutta methods [PDF]
, 2000 summary:We illustrate the use of the recent approach by P. Albrecht to the derivation of order conditions for partitioned Runge-Kutta methods for ordinary differential ...
Vermiglio, Rossana +2 more
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Modifying Runge – Kutta methods with higher order derivative approximations [PDF]
مجلة التربية والعلم, 1970 In this paper, we modify some sort of Runge-Kutta methods developed by David and Olin which needless function evaluation than ordinary corresponding Runge-Kutta methods.
Bashir Khlaf, Ghanim Abdullah
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Explicit two-step Runge-Kutta methods [PDF]
, 1995 summary:The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described.
Zennaro, Marino +2 more
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A class of implicit-explicit two-step Runge-Kutta methods [PDF]
, 2012 This work develops implicit-explicit time integrators based on two-step Runge-Kutta methods. The class of schemes of interest is characterized by linear invariant preservation and high stage orders.
Zharovski, Evgeniy, Sandu, Adrian
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Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2016 In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
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Order conditions of stochastic Runge-Kutta methods by B-series [PDF]
, 2000 In this paper, general order conditions and a global convergence proof are given for stochastic Runge-Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied
Burrage, Pamela +3 more
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Efficient explicit time integration for the simulation of acoustic and electromagnetic waves [PDF]
, 2015 The efficient and accurate numerical simulation of time-dependent wave phenomena is of fundamental importance in acoustic, electromagnetic or seismic wave propagation.
Mehlin, Michaela
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On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods [PDF]
, 1997 Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystrom (IRKN) methods for the numerical solution of systems of second-order differential equations.
De Meyer, H +7 more
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