Gegenbauer加法定理截断误差界的估计  

ESTIMATION FOR THE TRUNCATION ERROR BOUND OF GEGENBAUER'S ADDITION THEOREM

作　　者：肖玉萍 孟文辉 Xiao Yuping;Meng Wenhui(School of Mathematics,Northwest University,Xi'an 710127)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《高等学校计算数学学报》2022年第4期383-394,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11201373)。

摘　　要：1引言Bessel函数是在物理和工程中应用较为广泛的一类函数,德国天文学家F.W.Bessel早在18^(2)4年就第一次提出了该函数.Bessel函数是Bessel微分方程x^(2)d^(2)y/dx^(2)+xdy/dx+(x^(2)-m^(2))y=0,(1)的级数解,Bessel方程是在柱坐标或球坐标下使用分离变量法求解Laplace方程和Helmholtz方程时得到的.Gegenbauer's addition theorem of Bessel function has been widely used in acoustic and electromagnetic scattering problems,especially in solving 3-D scattering problems by using fast multipole method.Based on the asymptotic bounds of Bessel and Neumann functions,this paper estimates the truncation error of Gegenbauer's addition theorem,explicit bound and convergence order of the truncation error are obtained.The result is tested by some examples,which shows that the estimate is valid and sharp.

关 键 词：BESSEL函数 HELMHOLTZ方程 LAPLACE方程 分离变量法 截断误差 球坐标 级数解 加法定理 

分 类 号：O241.5[理学—计算数学]