Error Estimation and Control for ODEs SpringerLink
Derivative Runge-Kutta method (TDRK) for the numerical solution of first order Initial Value Problems (IVPs) is developed. Using the trigonometrically-fitting technique, an embedded …... THIRD-ORDER 2N-STORAGE RUNGE-KUTTA SCHEMES WITH ERROR CONTROL Mark H. Carpenter _ Christopher A. Kennedy t Abstract A family of four-stage third-order explicit Runge-Kutta schemes is derived that requires only two
Embedded Pair of Diagonally Implicit Runge-Kutta Method
high order embedded runge-kutta scheme for adaptive step-size control in the interaction picture method stephane balac´ ueb, universite ´europeenne de bretagne, universit´e de rennes i, france... ation of a 5th order Runge-Kutta method with embedded 4th order method, valid for general systems of diﬀerential equations, using just a plain 2.3 GHz Personal Computer.
Embedded explicit Runge-Kutta type methods for directly
This article is about the numerical solution of initial value problems for systems of ordinary differential equations. At first these problems were solved with a fixed method and constant step size,... digital design principles and practices 4th edition pdf download proved that an explicit Runge-Kutta formula of order p can be evaluated on Ip/2] processors, in an amount of time equivalent to p sequential stages, the minimum amount of time possible (also
A block 6(4) Runge-Kutta formula for nonstiff initial
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides, ACM Transactions on Mathematical Software 16, 201--222. Dormand, J. R. and Prince, P. J. (1980) A family of embedded Runge-Kutta formulae, J. Comput. physics formula pdf ebook download Abstract. AbstractA family of embedded Runge-Kutta formulae RK5 (4) are derived. From these are presented formulae which have (a) ‘small’ principal truncation terms in the fifth order and (b) extended regions of absolute stability
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Explicit General Linear Methods with Inherent Runge–Kutta
- A family of embedded Runge-Kutta formulae (1980) CiteSeerX
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A Family Of Embedded Runge Kutta Formulae Pdf
formula, several other embedded Runge-Kutta formulas have been found. Many practitioners were at one time wary of the robustness of Runge-Kutta- Fehlberg methods.
- When the stepsize in Runge-Kutta codes is restricted by stability, an uneven pattern of stepsizes with many step rejections is frequently observed. A modified strategy is proposed to smooth out this type of behaviour. Several new estimates for the dominant eigenvalue of the Jacobian are derived. It
- For the fifth-order case, explicit Runge-Kutta formulas have been found whose remainder, while of order six when y is present in (1), does become of order seven when / is a function of x alone , .
- Abstract. AbstractA family of embedded Runge-Kutta formulae RK5 (4) are derived. From these are presented formulae which have (a) ‘small’ principal truncation terms in the fifth order and (b) extended regions of absolute stability
- Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations by Christopher A. Kennedy , Mark H. Carpenter , R. Michael Lewis , 2000 The derivation of low-storage, explicit Runge–Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier–Stokes equations via direct numerical simulation.