Adrián Németh

57191244465

Publications - 3

EXPLICIT strong stability preserving multistep runge-kutta methods

Christopher Bresten Daniel Higgs Zachary Grant Adrián Németh Sigal Gottlieb David Ketcheson

Publication Name: Mathematics of Computation

Publication Date: 2017-01-01

Volume: 86

Issue: 304

Page Range: 747-769

Description:

High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.

Open Access: Yes

DOI: 10.1090/mcom/3115

Strong stability preserving explicit linear multistep methods with variable step size

Yiannis Hadjimichael Adrián Németh David Ketcheson Lajos Lóczi

Publication Name: SIAM Journal on Numerical Analysis

Publication Date: 2016-01-01

Volume: 54

Issue: 5

Page Range: 2799-2832

Description:

Strong stability preserving (SSP) methods are designed primarily for time integration of nonlinear hyperbolic PDEs, for which the permissible SSP step size varies from one step to the next. We develop the first SSP linear multistep methods (of order two and three) with variable step size, and prove their optimality, stability, and convergence. The choice of step size for multistep SSP methods is an interesting problem because the allowable step size depends on the SSP coefficient, which in turn depends on the chosen step sizes. The description of the methods includes an optimal step-size strategy. We prove sharp upper bounds on the allowable step size for explicit SSP linear multistep methods and show the existence of methods with arbitrarily high order of accuracy. The effectiveness of the methods is demonstrated through numerical examples.

Open Access: Yes

DOI: 10.1137/15M101717X

On the control of a vehicle dynamics problem

Tihamér A. Kocsis Adrián Németh Zoltán Horváth

Publication Name: 2014 IEEE International Electric Vehicle Conference Ievc 2014

Publication Date: 2014-01-01

Volume: Unknown

Issue: Unknown

Page Range: Unknown

Description:

In this paper we present an approach to find the controlled invariant sets of a nonlinear dynamical system. Our method explores the state space and determines the set of those initial values where the system can be stabilized with a bounded control function. A continuous closed-loop feedback rule can also be obtained from this procedure. We illustrate the numerical results of our method on a problem describing the behaviour of actuators controlling the lateral dynamics of a vehicle.

Open Access: Yes

DOI: 10.1109/IEVC.2014.7056192