On implicit Runge-Kutta methods for parallel computations
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On implicit Runge-Kutta methods for parallel computations

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Published by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va .
Written in English


  • Runge-Kutta formulas.,
  • Parallel computers.

Book details:

Edition Notes

Other titlesOn implicit Runge Kutta methods for parallel computations.
StatementStephen L. Keeling.
SeriesICASE report -- no. 87-58., NASA contractor report -- 178366., NASA contractor report -- NASA CR-178366.
ContributionsLangley Research Center.
The Physical Object
Pagination1 v.
ID Numbers
Open LibraryOL18032352M

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These relations are valid fo r Runge-Kutta methods, whether implicit or explicit, from firs t order method (e.g. Euler method) to fifth order method (e.g. Fehlberg method [9,12]). In all the Author: Andrés Granados. The theorem "implicit methods are better" (which should not to be pure theorem) is seen in case 3 of symmetric problems. All symmetric Runge-Kutta methods must be implicit. Hovewer, its a reason why Runge-Kutta is not so popular here. Parallel two-step Runge-Kutta methods Helmut Podhaisky, [email protected] Martin–Luther–University Halle–Wittenberg, Germany 20 July Outline Runge–Kutta and multi-step methods Explicit parallel peer methods Implicit parallel peer methods Summary. To be A-stable, and possibly useful for stiff systems, a Runge–Kutta formula must be is a significant computational advantage in diagonally implicit formulae, whose coefficient matrix is lower triangular with all diagonal elements by:

John Butcher’s tutorials Introduction to Runge–Kutta methods Φ(t) = 1 γ(t) application area, attention moved to implicit methods. Introduction to Runge–Kutta methods. Introduction Formulation Taylor series: exact solution Approximation Order conditions A few years File Size: KB. Diagonally Implicit Runge-Kutta Methods for Ordinary Di erential Equations. A Review Christopher A. Kennedy Private Professional Consultant, Palo Alto, California Mark H. Carpenter Langley Research Center, Hampton, Virginia National Aeronautics and Space Administration Langley Research Center Hampton, Virginia March A Parallel numerical method is developed. To analyze the convergent rate of the method, an explicit Runge-Kutta and an implicit DDADI methods are introduced and compared in the parallel computations. The results show that the DDADI method performs better than the Runge-Kutta method : San-Yih Lin, Zhong Xin Yu. The class of collocation methods from the previous section are a subset of the class of Runge-Kutta methods. Local accuracy of Runge-Kutta methods We will now investigate the accuracy of the methods introduced above in terms of their approxi-mation of the numerical solution over one timestep.

GPU Implementation of Implicit Runge-Kutta Methods Navchetan Awasthi, Abhijith J Supercomputer Education and Research Centre Indian Institute of Science, Bangalore, India [email protected], [email protected] Abstract—Runge-Kutta methods are an important family of implicit and explicit iterative methods used for the approximation. Runge–Kutta methods a re the 4-stage methods of order 4, derived by Kutta [6]. Their coefficients are presented in Table 1 (a ij as a matrix, c i in the left column, and b j in the bottom row). I was asked to work out a differential equation using the Euler method and then followed by the Runge-Kutta method. Based on the theory I have come across it says that the Euler method agrees with the. moved to diagonally and singly implicit methods. Runge–Kutta methods for ordinary differential equations – p. 5/ With the emergence of stiff problems as an important application area, attention moved to implicit methods. Methods have been found based on Gaussian quadrature.