We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on adaptive time-grids, while maintaining high orders. Classical such as Jacobi or Gauss-Seidel are typically either converge quickly. present a novel method utilizing asynchronous communication techniques to get both pro...

Dynamical low-rank approximation by tree tensor networks is studied for the data-sparse of large time-dependent data tensors and unknown solutions to differential equations. A time integration method prescribed rank presented analyzed. It extends known projector-splitting integrators dynamical matrices rank-constrained Tucker shown inherit their favorable properties. The integrator based on rec...

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is ex...

Symplectic methods for Hamiltonian systems are known to have favourable properties concerning long-time integrations (no secular terms in the error of the energy integral, linear error growth in the angle variables instead of quadratic growth, correct qualitative behaviour) if they are applied with constant step sizes, while all of these properties are lost in a standard variable step size impl...

in the present time, phenomenon like globalization, regionalism and economic integration are the basic issues which bring many positive consequences to the world economy. regionalism and economic integration are one of the ways that developing countries can adopt to collate the globalization process. to acknowledge their own abilities or, to settle the commercial and economic disputes in their ...