Liouville-Green变换在数值解双参数二阶常微分方程第一边值问题中的应用  

APPLICATION OF LIOUVILLE-GREEN TRANSFORMATION IN NUMERICAL SOLUTION OF THE FIRST BOUNDARY VALUE PROBLEM OF THE SECOND-ORDER ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

作　　者：王国英[1] 

机构地区：[1]南京大学

出　　处：《高等学校计算数学学报》1992年第1期21-28,共8页Numerical Mathematics A Journal of Chinese Universities

摘　　要：一 引 言 双参数问题在实际问题中有广泛的应用。关于双参数微分方程边值问题渐近解的讨论最近二十年来已作了不少工作。Applying Liouville-Green transformation, we establish a high accurate uniformly convergent difference scheme for -ey' + ua(x)y' + b(x)y = f(x), where a ( x )≥al > 0,b(x)≥b1>0,a(x),b(x) and f(x) smooth for 0≤x≤1,e,u be positive small parameters, y(0) and y(l) given. We prove that the solution of this scheme converges to that of the differential equation problem uniformly in e,u with order h3 (h denotes a mesh step.) Finally, numerical results for the scheme are given.

关 键 词：L-G变换 常微分方程 差分格式 

分 类 号：O241.81[理学—计算数学]