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Computational Mathematics and Modeling

, Volume 18, Issue 1, pp 19–28 | Cite as

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

  • D. S. Filippychev
Article
  • 21 Downloads

Abstract

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.

Keywords

Cauchy Problem Boundary Function Asymptotic Solution Trivial Solution Singular Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media, Inc. 2007

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  • D. S. Filippychev

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