Runge-Kutta Methods
Oscillation of Runge Kutta methods for advanced impulsive differential equations with piecewise constant arguments
... and nonoscillation for Runge-Kutta methods are obtained. In Section , the conditions of oscillation and nonoscillation for θ -methods are obtained. Moreover, it is proved that the oscillation ...
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A class of Runge–Kutta methods for nonlinear Volterra integral equations of the second kind with singular kernels
... This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind. In order to solve nonlinear ...
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2-stage explicit total variation diminishing preserving Runge-Kutta methods
... explicit Runge-Kutta methods of order two (RK2) when ap- plied to the numerical solution of special nonlinear initial value problems (IVPs) for ...
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Interval structure of Runge-Kutta methods for solving optimal control problems with uncertainties
... Interval methods have been introduced over the years ...of Runge- Kutta methods have been analyzed in [19, ...Since, Runge-Kutta methods have a significant role in the ...
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New rational and pseudo type runge kutta methods for first order initial value problems
... rational methods and non-linear methods based on mean expressions are not as popular as conventional numerical methods ...multistep methods and Runge-Kutta methods), they ...
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Dissipativity of Runge Kutta methods for a class of nonlinear functional integro differential equations
... of Runge-Kutta methods [] and one-leg methods [] for this kind of problems, ...one-leg methods for FIDEs ...of Runge-Kutta methods for ...
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Monotonicity and Boundedness in general Runge-Kutta methods
... 4 Illustrating our General Procedure III in a search for some optimal singly-diagonally-implicit Runge-Kutta methods. 83[r] ...
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A Comparative Study on Fourth Order and Butcher’s Fifth Order Runge-Kutta Methods with Third Order Initial Value Problem (IVP)
... order Runge-Kutta methods, also in [3] the author presented a comparative study on numerical solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and ...
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Stepsize Selection in Explicit Runge Kutta Methods for Moderately Stiff Problems
... explicit Runge-Kutta method that is suitable when solving moderately stiff differential ...for Runge-Kutta methods of third and fourth order demonstrate the properties and capabilities ...
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Numerical stability and oscillation of the Runge Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type
... stability region of Runge-Kutta methods is determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained. A necessary and sufficient ...
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Global error estimation of linear multistep methods through the Runge-Kutta methods
... embedded Runge-Kutta methods. In the case of PC methods that predictor is an Adams-Bashforth scheme of order p and cor- rector is an Adams-Moulton scheme of the same order, the Milne ...
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A New 4th Order Hybrid Runge-Kutta Methods for Solving Initial Value Problems (IVPs)
... derivative method using the usual arithmetic mean respectively. Akanbi [5] developed a third-order method based on the geometric mean. But [6] and [7] introduced the concept of the heronian mean Evans and Yaacob [8] ...
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A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity
... of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic ...of Runge-Kutta ...of ...
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Two Implicit Runge Kutta Methods for Stochastic Differential Equation
... Recently, many scholars have successfully derived some methods for SDEs for both Itô and Stratonovich forms. Burrage and Burrage [1-3] established the colored rooted tree theory and Stochastic B-series expansion. ...
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Design and Analysis of Some Third Order Explicit Almost Runge Kutta Methods
... Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, ...The methods are derived through the application of order and stability conditions normally associated with ...
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Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models
... Split-explicit methods typically divide the dynamics into three groups: fast vertical waves that are treated implicitly, fast horizontal waves that are substepped relative to the other dynamics with an explicit ...
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Preconditioning of implicit Runge-Kutta methods
... Abstract. A major problem in obtaining an efficient implementation of fully implicit Runge-Kutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of ...
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High Order Explicit Two-Step Runge-Kutta Methods for Parallel Computers
... Numerical experiments with 4- and 5-stage methods show the influence of this superconvergence condition. However, in general it is not possible to employ the new introduced weights to improve the stability of high ...
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ORDER OF THE RUNGE-KUTTA METHOD AND EVOLUTION OF THE STABILITY REGION
... 4. Feagin T. A tenth-order Runge–Kutta method with error estimate. In: Proc. of the IAENG Conf. on Scientific Computing. Hong Kong, 2007. Accessible at https://sce.uhcl.edu/feagin/courses/rk10.pdf 5. Feagin ...
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