Functional continuous Runge–Kutta–Nyström methods
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nyström for second-order ordinary differential equations with
Alexey Eremin
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Strong approximation for Itô stochastic differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2015 In this paper, a class of semi-implicit two-stage stochastic Runge-Kutta methods (SRKs) of strong global order one, with minimum principal error constants are given.
Mehran Namjoo
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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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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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Spatially partitioned embedded Runge-Kutta Methods [PDF]
, 2013 We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain.
Ketcheson, D. I. +2 more
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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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Optimal monotonicity-preserving perturbations of a given Runge-Kutta method [PDF]
, 2018 Perturbed Runge--Kutta methods (also referred to as downwind Runge--Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge--Kutta counterparts.
Higueras, Inmaculada +2 more
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Volume preservation by Runge–Kutta methods [PDF]
Applied Numerical Mathematics, 2016 17 pages, as submitted to ...
Bader, Philipp +3 more
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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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Parallel Implicit Runge-Kutta Methods for Stiff ODEs [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2004 The main objective of this paper is to develop and construct numerical algorithms for solving stiff system of ordinary differential equations (ODEs) which are suitable for running on parallel computers (MIMD computers).Semi-parallel implicit Runge-Kutta ...
Bashir Khalaf, Abdulhabib Murshid
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