Abstract A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a piecewise linear function t the test space based on discontinuous constant functions. We prove that proposed has convergence order $$O(\tau ^{1+ \alpha }), \, \in (0, 1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/Mat...

Abstract. In this paper we propose a new parareal algorithm for parallelizing in time molecular dynamics problems. The original structure of this algorithm allows one to consider multi-time stepping, namely two levels of temporal discretization, providing a larger range for the fine and coarse solvers definition. We also prove the symplecticity of this method, which is an expected behavior of t...

Rigid multibody dynamics with friction and impact are ill-posed. The rigidity assumption can be responsible for large null-spaces. By describing the multibody system with springs switching on and off in a variational inequality setting, the solutions are smooth and the behaviour in the stiff limit can be analyzed. From the limiting process it becomes apparent that the regularized solution conve...

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial di erential equations. Termed TVD (total variation diminishing) time discretizations before, this class of high-order time discretization methods preserves the strong-stability properties of rst-order Euler time step...

In this paper, we will present a generalized convolution quadrature for solving linear parabolic and hyperbolic evolution equations. The original convolution quadrature method by Lubich works very nicely for equidistant time steps while the generalization of the method and its analysis to non-uniform time stepping is by no means obvious. We will introduce the generalized convolution quadrature ...

By introducing Colpitts oscillator as a chaotic system, this paper deals with back-stepping control method and investigates the restrictions and problems of the controller where non-existence of a suitable response in the presence of uncertainty is the most important problem to note. In this paper, the back-stepping sliding mode method is introduced as a robust method for controlling nonlinear ...