Finite Difference Methods,Theory and Applications

This volume is the Proceedings of the First Conference on Finite Difference Methods which was held at the University of Rousse, Bulgaria, 10--13 August 1997. The conference attracted more than 50 participants from 16 countries. 10 invited talks and 26 contributed talks were delivered. The volume contains 28 papers presented at the Conference. The most important and widely used methods for solution of differential equations are the finite difference methods. The purpose of the conference was to bring together scientists working in the area of the finite difference methods, and also people from the applications in physics, chemistry and other natural and engineering sciences.

[1]  Allaberen Ashyralyev,et al.  Finite Difference Method for Delay Parabolic Equations , 2011 .

[2]  Alexander Zlotnik,et al.  On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side , 2002 .

[3]  Matthias Ehrhardt,et al.  Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability , 2003 .

[4]  Alexander Zlotnik,et al.  On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation , 2009 .

[5]  Matthias Ehrhardt,et al.  Discrete transparent boundary conditions for the Schrödinger equation , 2001 .

[6]  I. Zlotnik.  Family of finite-difference schemes with approximate transparent boundary conditions for the generalized nonstationary Schrödinger equation in a semi-infinite strip , 2011 .

[7]  Allaberen Ashyralyev,et al.  Well-posedness of delay parabolic difference equations , 2014 .

[8]  A. Zlotnik,et al.  Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis , 2014, 1406.5102.

[9]  Xiaonan Wu,et al.  Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip , 2010, J. Comput. Appl. Math..

[10]  Deniz Agirseven,et al.  Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition , 2012 .

[11]  Alexander A. Zlotnik,et al.  Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation , 2013, ENUMATH.

[12]  B. Ducomet,et al.  On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. Part II , 2006 .

[13]  Xiaonan Wu,et al.  Analysis of finite element method for one-dimensional time-dependent Schrödinger equation on unbounded domain , 2008 .