tailieunhanh - báo cáo hóa học:" Research Article A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term"

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 A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 781750 16 pages doi 2010 781750 Research Article A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term Jinsong Hu 1 Youcai Xu 2 and Bing Hu2 1 School of Mathematics and Computer Engineering Xihua University Chengdu 610039 China 2 School of Mathematics Sichuan University Chengdu 610064 China Correspondence should be addressed to Youcai Xu xyc@ Received 24 August 2010 Accepted 14 November 2010 Academic Editor V. Shakhmurov Copyright 2010 Jinsong Hu 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. We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energy method. Numerical simulations verify that the method is accurate and efficient. 1. Introduction A symmetric version of regularized long wave equation SRLWE ut Px uux - uxxt - 0 Pt Ux 0 has been proposed to model the propagation of weakly nonlinear ion acoustic and space charge waves 1 . The sec2 solitary wave solutions are u x f 3 v2 - 1 v 2 sec2 v2 - v2 x - vi 1 2 1 3 v2 1 _21 v2 - 1 ._ p x t --v2---sec2 2 Y v2 x - vt . 2 Boundary Value Problems The four invariants and some numerical results have been obtained in 1 where v is the velocity v2 1. Obviously eliminating p from we get a class of SRLWE Utt - uxx 2 u2 t - uxxtt 0. Í1-3 Equation is explicitly symmetric in the x and t derivatives and is very similar to the regularized long wave equation that .