Klein-Gordon方程初达值问题的一个新的守恒差分格式  

A NEW CONSERVAIVE FINITE DIFFERENCE SCHEME FOR AN INITIAL-BOUNDARY VALUE PROBLEM OF A NONLINEAR KLEIN-GORDON EQUATION

作　　者：张鲁明[1] 常谦顺[1] 

机构地区：[1]中国科学院应用数学研究所,北京100080

出　　处：《应用数学学报》1999年第4期531-540,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金

摘　　要：本文对非线性Klein－Gordon（NKG）方程的初边值问题提出了一种新的差分格式，它保持了NKG方程初边值问题的能量守恒．证明了该格式的收敛性和稳定性．特别地，由于该格式是完全隐式的，故对求长时解有着重要的作用．数值计算结果表明该方法计算速度快，精度好．In this paper, a new finite difference scheme is proposed for solving an initialboundary value problem of a nonlinear Klein-Gordon equation. The scheme has an advantage of conservating discrete energy, just as the initial-boundary value problem conservate energy. And its convergence and stablity are proved. Because of the numerical scheme is fully impllcit, it has particularly important function when long time solutions are sought. The ressSult of numerical compution shows that the new scheme is very accurate and fast.

关 键 词：能量守恒 差分格式 初边值问题 K-G方程 

分 类 号：O241.82[理学—计算数学]