Generalizing recent results in [M. K. Camlibel, Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems, Ph.D. thesis, Center for Economic Research, Tilburg University, Tilburg, The Netherlands, 2001], [M. K. Camlibel, W. P. M. H. Heemels, and J. M. Schumacher, IEEE Trans. Circuits Systems I: Fund. Theory Appl., 49 (2002), pp. 349–357], and [J.-S. Pang and D. Stewart, Math...

Analytical and experimental convergence results are presented for a novel pseudo-unsteady solution method for higher-order accurate upwind discretizations of the steady Euler equations. Comparisons are made with an existing pseudo-unsteady solution method. Both methods make use of nonlinear multigrid for acceleration and nested iteration for the fine-grid initialization. The new method uses ite...

In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature, from modelling pattern formation in developmental biology to cancer research, wound healing, tissue and bone regeneration and cell motility. Therefore, it is...

1 OVERVIEW In our paper, we present asynchronous time integration to simulate uids using a non-iterative EOS-based SPH solver. In this document, we provide additional images for comparison to previous methods (Sec. 2) and a quantitative velocity study of the time stepping methods (Sec. 3). Results are presented for xed time stepping (FTS), globally adaptive time stepping (GTS) [Desbrun and Gasc...

This paper reviews the main properties, and most recent developments, of Krylov subspace spectral (KSS) methods for time-dependent variable-coefficient PDE. These methods use techniques developed by Golub and Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral domain in order to achieve high-order accuracy in time and stability characteristic of im...

Nowadays, the design of so-called consistent time-stepping schemes that basically feature a physically correct time integration, is still a state-of-the-art topic in the area of numerical mechanics. Within the proposed framework for finite elastoplasto-dynamics, the spatial as well as the time discretisation rely both on a Finite Element approach and the resulting algorithmic conservation prope...

The modified Szabo wave equation is one of the various models that have been developed to model the power law frequency-dependent attenuation phenomena in lossy media. The purpose of this study is to develop two different efficient numerical methods for the two-dimensional Szabo equation and to compare the relative merits of each method. In both methods we employ the ADI scheme to split directi...

This paper deals with time stepping schemes for the Cahn–Hilliard equation three different types of dynamic boundary conditions. The proposed first and second order are mass-conservative energy-dissipative – as they based on a formulation coupled system partial differential equations allow spatial discretizations in bulk boundary. latter enables refinements without an adaptation mesh interior d...

Forward transient electromagnetic modeling requires the numerical solution of a linear constant-coefficient initial-value problem for the quasi-static Maxwell equations. After discretization in space this problem reduces to a large system of ordinary differential equations, which is typically solved using finite-difference time-stepping. We compare standard time-stepping schemes such as the exp...

In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor– Galerkin schemes introduced in Refs. 6 and 7 (particularly wavelet Taylor–Galerkin scheme based on Crank–Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori esti...