The main di culty in the implementation of most standard implicit Runge-Kutta (IRK) methods applied to (sti ) ordinary di erential equations (ODE's) is to e ciently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is ba...

Using a slightly diierent discretization scheme in time and adapting the approach in Nochetto et al: (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowey (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piece-wise linear nite element approximation of a model for phase separation of a mul...

This article presents a reinforcement learning framework for continuous-time dynamical systems without a priori discretization of time, state, and action. Based on the Hamilton-Jacobi-Bellman (HJB) equation for infinite-horizon, discounted reward problems, we derive algorithms for estimating value functions and improving policies with the use of function approximators. The process of value func...

In this paper a variant of nonlinear exponential Euler scheme is proposed for solving heat conduction problems. The method based on iterations where at each iteration linear initial-value problem has to be solved. We compare the backward combined with iterations. For both methods we show monotonicity and boundedness solutions give sufficient conditions convergence Numerical tests are presented ...

This paper presents a backward Euler stabilized-based control strategy applied to a neutral point clamped (NPC) back-to-back connected five level converters. A generalized method is used to obtain the back-to-back NPC converter system model. The backward Euler stabilized-based control strategy uses one set of calculations to compute the optimum voltage vector needed to reach the references and ...

In this paper, we propose an implicit gradient descent algorithm for the classic k-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch gradient in every iteration. It is the average of the fixed-point trajectory that is carried over to the next gradient step. We draw connections between the proposed...

Abstract We analyze backward Euler time stepping schemes for a primal DPG formulation of class parabolic problems. Optimal error estimates are shown in natural norm and the L 2 {L^{2}} field variable. For heat equation solution our equals standard Galerkin scheme and, thus, optimal bound...

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for integration of system of algebraic and differential equations in general, the scheme is primarily developed for use with direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed...

In this paper, the stability and accuracy properties of exponentially-t integration algorithms applied to the test problem x= ?Ax are compared to the more standard backward-Euler and semi-implicit methods. For the analysis, A 2 R nn is assumed to be connectedly diagonally-dominant with positive diagonals, as this models the equations resulting from the way MOS transistors and interconnect paras...

In this talk we introduce a family of numerical approximations for the stochastic differentialequations (SDEs) with, possibly, no-globally Lipschitz coefficients. We show that for a given Lyapunovfunction V : R → [1,∞) we can construct a suitably tamed Euler scheme that preserves so calledV-stability property of the original SDEs without imposing any restrictions on the time dis...