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Showing 1 to 20 of 171 for “"Runge–Kutta"”.
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SARK: a type-insensitive Runge-Kutta code
A novel solution method based on Mono-implicit Runge-Kutta methods has been fully developed and analysed for the numerical solution of stiff systems of ordinary differential equations (ODE). These Backward Runge-Kutta (BRK) methods have very desirable stability properties which make them efficient …
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Συνεχείς επεκτάσεις μεθόδων Runge-Kutta για προβλήματα αρχικών τιμών
… in order to produce continuous extensions of Runge-Kutta algorithms when solving initial value problems. We consider two ways (I) scaling (II) interpolation. The same extension was done for Runge-Kutta-Nystrom methods for initial value problem of second class.
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Stability and efficiency properties of implicit Runge-Kutta methods
… certain stability properties of implicit Runge-Kutta methods. In particular, a new stability property is defined, which is a modification to non-autonomous problems of A-stability, and its relation to B-stability is considered. A Runge-Kutta method is written as [see 01front.pdf for …
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Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation
In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic …
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Effiziente Implementierung eingebetteter Runge-Kutta-Verfahren durch Ausnutzung der Speicherzugriffslokalität
Eingebettete Runge-Kutta-Verfahren zählen zu den numerischen Lösungsverfahren für nichtsteife Anfangswertprobleme gewöhnlicher Differentialgleichungssysteme. Sie werden in der Praxis häufig eingesetzt, da sie gute numerische Eigenschaften aufweisen, eine effiziente Steuerung der Schrittweite …
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Reduktion des Kommunikationsaufwands iterierter Runge-Kutta-Verfahren für dünnbesetzte gewöhnliche Differentialgleichungssysteme
Iterierte Runge-Kutta (IRK) Verfahren sind eine Klasse von Lösungsverfahren für Anfangswertprobleme gewöhnlicher Differentialgleichungssysteme (DGL), welche ein hohes Parallelisierungspotential besitzen. Während Implementierungen für dichtbesetzte DGL regelmäßig Vektoren der Größe der DGL …
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Two step runge-KUTTA-nystrom method for solving second-order ordinary differential equations
… but it lengthens the execution time. Two-Step Runge-Kutta (TSRK) method were derived to solve first-order Ordinary Differential Equations (ODE). The order conditions of TSRK method were obtained by using Taylor series expansion. The explicit TSRK method was derived and its stability were …
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The analysis and implementation of exponential almost Runge-Kutta methods for semilinear problems
… Methods and the multi-stage Exponential Runge-Kutta Methods. A broader framework of Exponential General Linear Methods builds on these two families. We extend the classical Almost Runge-Kutta Method family, of multi-stage multi-value schemes, into an EI formulation, developing a new …
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The Runge-Kutta Taylor-SPH model, a new improved model for soil dynamics problems
… behaviors and presents three versions: - The Runge-Kutta Taylor-SPH for analysis of dry soils behavior in dynamic (small deformation theory) - The new Runge-Kutta Taylor-SPH for analysis of dry soils behavior in dynamic (large deformation theory) - The v - pw Runge-Kutta Taylor-SPH for …
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A dynamic multiscale viscosity algorithm for shock capturing in Runge Kutta Discontinuous Galerkin methods
In order to improve the performance of higher-order Discontinuous Galerkin finite element solvers, a shock capturing procedure has been developed for hyperbolic equations. The Dynamic Multiscale Viscosity method, originally presented by Oberai and Wanderer [8, 9] in a Fourier Galerkin context, is …
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Stability analysis of the 4th order Runge Kutta method in application to colloidal particle interactions
… of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability …
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A Runge Kutta Discontinuous Galerkin-Direct Ghost Fluid (RKDG-DGF) Method to Near-field Early-time Underwater Explosion (UNDEX) Simulations
… in the ALE description is discretized by a Runge Kutta Discontinuous Galerkin (RKDG) method. For multi-fluid flows, a Direct Ghost Fluid (DGF) Method coupled with the Level Set (LS) interface method is incorporated in the RKDG framework. The combination of RKDG and DGF methods (RKDG-DGF) is …
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Numerical Simulations of Viscoelastic Flows Using the Discontinuous Galerkin Method
… optimal third-order total-variation diminishing Runge-Kutta scheme is used for the temporal discretization of the Oldroyd-B equation. The overall accuracy in time is therefore limited to second-order due to the Crank-Nicolson scheme; however, a third-order Runge-Kutta scheme is implemented for …
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A comparison of numerical algorithms for solution of the transient stability problem
… The five algorithms studied are: fourth-order Runge-Kutta; state transition; the trapezoidal rule; Adams-Moulton predictor-corrector; and Hamming predictor-corrector. The five algorithms, using various step sizes, are applied to three test systems, including the IEEE l4-bus system, using a …
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Multimethods for the Efficient Solution of Multiscale Differential Equations
… these issues. First, new implicit multirate Runge–Kutta methods are analyzed with a special focus on stability. This is extended into implicit multirate infinitesimal methods. We introduce approaches for constructing implicit-explicit methods based on Runge–Kutta and general linear methods. …
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MATLODE: A MATLAB ODE Solver and Sensitivity Analysis Toolbox
… methods are implemented, namely explicit Runge-Kutta, implicit Runge-Kutta, Rosenbrock, and single diagonally implicit Runge-Kutta. Each approach and family has its own strengths and weaknesses when applied to real world problems. MATLODE has a multitude of options that allows users to …
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Método gráfico para establecer el campo de pendientes de una Ecuación Diferencial
… diferencial. Presenta los métodos de Euler, Runge-Kutta de cuarto orden y el método multipasos de Adams-Bashforth-Moulton. Asimismo, se explica las ecuaciones mediante el uso del software para los métodos gráficos tales como el Maple y Geogebra. ABSTRACT: Oriented work in the area of …
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Data Reduction Procedure for an Experimental Method of Measuring the Velocity-Coupled Response Function of Solid Propellants
… <p>The data reduction program consists of a Runge-Kutta routine driven by a BFGS multivariable search routine. The Runge-Kutta routine determines the pressure distribution within the chamber of the proposed apparatus for a specific velocity-coupled response function (Rv). The BFGS …
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Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and Wofbrandt, …
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Speeding up high-order algorithms in computational fluid and kinetic dynamics: based on characteristics tracing and low-rank structures
… is the development of a new Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion problems. Eulerian-Lagrangian and semi-Lagrangian methods have become popular ways to solve hyperbolic conservation laws due to their ability to allow large …
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