tailieunhanh - Báo cáo hóa học: "Research Article Maximal Regularity of the Discrete Harmonic Oscillator Equation"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Maximal Regularity of the Discrete Harmonic Oscillator Equation | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 290625 14 pages doi 2009 290625 Research Article Maximal Regularity of the Discrete Harmonic Oscillator Equation Airton Castro 1 Claudio Cuevas 1 and Carlos Lizama2 1 Departamento de Matematica Universidade Federal de Pernambuco Avenida. Professor. Luiz Freire S N 50540-740 Recife PE Brazil 2 Departamento de Matemdtica y Ciencia de la Computation Facultad de Ciencias Universidad de Santiago de Chile Casilla 307-Correo 2 9160000 Santiago Chile Correspondence should be addressed to Carlos Lizama Received 31 October 2008 Revised 27 January 2009 Accepted 9 February 2009 Recommended by Mariella Cecchi We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting and a characterization of Ip-maximal regularity or well posedness solely in terms of R-boundedness properties of the resolvent operator involved in the equation. Copyright 2009 Airton Castro et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In numerical integration of a differential equation a standard approach is to replace it by a suitable difference equation whose solution can be obtained in a stable manner and without troubles from round off errors. However often the qualitative properties of the solutions of the difference equation are quite different from the solutions of the corresponding differential equations. For a given differential equation a difference equation approximation is called best if the solution of the difference equation exactly coincides with solutions of the corresponding differential equation evaluated at a discrete sequence of points. Best approximations are not unique cf. 1 Section . In the recent