We provide a theoretical analysis of the processing technique for the numerical integration of ODEs. We get the effective order conditions for processed methods in a general setting so that the results obtained can be applied to different types of numerical integrators. We also propose a procedure to approximate the postprocessor such that its evaluation is virtually cost-free. The analysis is ...

To simulate the behaviour of a nuclear power reactor it is necessary to be able to integrate the time-dependent neutron diffusion equation inside the reactor core. In particular, we will consider here VVER-type reactors which use the neutron diffusion equation discretized on hexagonal meshes. Several algorithms to integrate the time dependent neutron diffusion equation have been developed, by m...

The prediction of long-term deformations of concrete and reinforced concrete structures has been a field of extensive research and several different creep models have been developed so far. Most of the models were developed for constant concrete stresses, thus, in case of varying stresses a specific superposition principle or time-integration, respectively, is necessary. Nowadays, when modeling...

The fair price of a financial option on an asset that follows a Poisson jump diffusion process satisfies a partial integro-differential equation. When numerical methods are used to solve such equations the integrals are usually evaluated using either quadrature methods or fast Fourier methods. Quadrature methods are expensive since the integrals must be evaluated at every point of the mesh. Tho...

Contents 1 Introduction 3 2 Description of the local time stepping strategy 4 2.

An explicit multi time stepping algorithm with applications to aerodynamic flows is presented. In the algorithm in different parts of the computational domain different time steps are taken, and the flow is synchronized at so-called synchronization levels. The algorithm is validated for aerodynamic turbulent flows. For two dimensional flows speedups in the order of five with respect to single t...

This paper presents a high-order finite element method for calculating elastic-plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame [1, 2]. In order to handle transition to plastic flow, we formulate the stress-strain relation in rate (or incremental) form...

Tremendous efforts have been made in the field of parallel numerical methods for ODE. Special volumes are dedicated to the theme we are going to discuss [1]. The brief survey of some classical results and recent developments is the aim of this paper. We particulary focus on small scale parallelism across the method, but not large scale parallelism across the system.

In this paper, numerical solution of first-order systems of ordinary differential equations (ODEs) is considered and an error estimation method is proposed. By this method, the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically. 20...

A three-dimensional simulation of an aerobraking maneuver is investigated using a dissipative timestepping algorithm. The system modelled consists of an atmospheric probe connected to an orbiter by a thin, elastic tether. A dissipative time-stepping scheme, developed from the generalised-alpha method, is used to accurately predict the highly nonlinear dynamics of the flexible system. The simula...