Accelerated Runge-Kutta Methods
Discrete Dynamics in Nature and Society, 2008 Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step ...
Firdaus E. Udwadia, Artin Farahani
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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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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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Positive and elementary stable explicit nonstandard Runge-Kutta methods for a class of autonomous dynamical systems [PDF]
International Journal of Computational Mathematics, 2017 In this paper, we construct and analyze explicit nonstandard Runge-Kutta (ENRK) methods which have higher accuracy order and preserve two important properties of autonomous dynamical systems, namely, the positivity and linear stability. These methods are
Q. A. Dang, M. T. Hoang
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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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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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Track parameter propagation through the application of a new adaptive Runge-Kutta-Nystrom method in the ATLAS experiment [PDF]
, 2008 In this paper we study several fixed step and adaptive Runge-Kutta methods suitable for transporting track parameters through an inhomogeneous magnetic field.
Bugge, L +3 more
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Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisations of the Maxwell equations [PDF]
, 2007 Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and ...
Botchev, M.A. +2 more
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