We propose two numerical methods for accelerating the convergence of the standard fixed point method associated with a nonlinear and/or degenerate elliptic partial differential equation. The first method is linearly stable, while the second is provably convergent in the viscosity solution sense. In practice, the methods converge at a nearly linear complexity in terms of the number of iterations...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

In these notes we present the pseudodifferential approach to elliptic boundary value problems for the Laplace operator acting on functions on a smoothly bounded compact domain in a compact manifold. This is an elaboration of the classical method of multiple layer potentials. After a short discussion of this method we consider the theory of homogeneous distributions on R. This is useful in our s...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

In this paper we study the Local Discontinuous Galerkin scheme for solving the stochastic heat equation driven by the space white noise. We begin by giving a brief introduction to stochastic processes, stochastic differential equations, and their importance in the modern mathematical context. From there, using an example stochastic elliptic partial differential equation, we approximate the whit...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

Über die statistische Beschreibung nichtstationärer Mobilfunkkanäle. In diesem Artikel wird die statistische Beschreibung von Mobilfunkkanälen behandelt, welche nicht die Annahme schwach stationärer unkorrelierter Streuer erfüllen. Besondere Beachtung hierbei findet die lokale Streufunktion. Die vorgestellten Methoden, welche besonders für schwach dispersive und schwach korrelierte Kanäle geeig...

We present a new dispersive analysis of the isospin breaking decay η → 3π. The resulting representation of the decay amplitude allows us to determine the quark mass double ratio Q and we find as a preliminary result Q = 22.3 ± 0.4. Finally, we discuss a number of improvements that we intend to implement in the future.