Randomised one-step time integration methods for deterministic operator differential equations

Extended one-step methods for solving delay-differential equations

We discuss extended one-step methods of order three for the numerical solution of delay-differential equations. A convergence theorem and the numerical studies regarding the convergence factor of these methods are given. Also, we investigate the stability properties of these methods. The results of the theoretical studies are illustrated by numerical examples.

Long-Time-Step Methods for Oscillatory Differential Equations

Considered are numerical integration schemes for nondissipative dynamical systems in which multiple time scales are present. It is assumed that one can do an explicit separation of the RHS “forces” into fast forces and slow forces such that (i) the fast forces contain the high frequency part of the solution, (ii) the fast forces are conservative, and (iii) the reduced problem consisting only of...

Higher-order operator splitting methods for deterministic parabolic equations

Analysis of Numerical Methods for Differential-Algebraic Equations: The one Step Methods

Abstract. Differential algebraic equations have wide applications in the field of engineering and science where the mathematical models form the descriptor systems. Analysis and modeling of the solutions of such systems need to handle with the different equations related to the systems. A time-domain discretization, for example, finite difference, finite volume, etc., may lead to DAEs of descri...

A Modified Multi Time Step Integration for Dynamic Analysis

In this paper new implicit higher order accuracy (N-IHOA) time integration based on assumption of constant time step is presented for dynamic analysis. This method belongs to the category of the multi time step integrations. Here, current displacement and velocity are assumed to be functions of the velocities and accelerations of several previous time steps, respectively. This definition causes...