A stability formula for Lax-Wendroff methods with fourth-order in time and general-order in space for the scalar wave equation
会议名称：《中国科学院地质与地球物理研究所第11届（2011年度）学术年会》
会议日期：2012年
学科分类：070801[理学-固体地球物理学] 07[理学] 0708[理学-地球物理学]
基 金：supported by National Natural Science Foundation of China under grant numbers 40974074 40774069 and 40830424
摘 要：Based on the formula for stability of finite-difference methods with second-order in time and general-order in space for the scalar wave equation,I obtain a stability formula for Lax-Wendroff methods with fourth-order in time and general-order in *** the formula for methods with second-order in time,this formula depends on two parameters:one parameter is related to the weights for approximations of second spatial derivatives;the other parameter is related to the weights for approximations of fourth spatial *** discretizing the mixed derivatives properly,the formula can be generalized to the case where the spacings in different directions are different. This formula can be useful in high-accuracy seismic modeling using the scalar wave equation on rectangular grids,which involves both high-order spatial discretizations and high-order temporal approximations.I also prove the instability of methods obtained by applying high-order finite-difference approximations directly to the second temporal derivative,and this result solves theBording’s conjecture.