Numerical solution of the differential equation describing the behavior of the zeroth-order boundary function

被引：0
作者：
Filippychev D.S.
机构：
来源：
Computational Mathematics and Modeling | 2007年 / 18卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Cauchy Problem; Boundary Function; Asymptotic Solution; Trivial Solution; Singular Part;
D O I：
10.1007/s10598-007-0003-2
中图分类号：
学科分类号：
摘要：
The asymptotic solution of the integro-differential plasma-sheath equation is considered. This equation is singularly perturbed because of the small coefficient multiplying the highest order (second) derivative. The asymptotic solution is obtained by the boundary function method. Equations are derived for the first two coefficients in the form of both a regular series expansion and an expansion in boundary functions. The equation for the first coefficient of the regular series has only a trivial solution. A numerical algorithm is considered for the solution of the second-order differential equation describing the behavior of the zeroth-order boundary function. The proposed algorithm efficiently solves the boundary-value problem and produces a well-behaved solution of the Cauchy problem. © 2007 Springer Science+Business Media, Inc.
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页码：19 / 28
页数：9
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