Computational Mathematics and Modeling

, Volume 17, Issue 4, pp 341–353 | Cite as

Applying the dual operator formalism to derive the zeroth-order boundary function of the plasma-sheath equation

  • D. S. Filippychev


The article constructs the asymptotic solution of the Tonks-Langmuir integro-differential equation with an Emmert kernel, which describes the potential both in the bulk plasma and in a narrow boundary layer. Equations of this type are singularly perturbed, because the highest order (second) derivative is multiplied by a small coefficient. The asymptotic solution is obtained by the boundary function method. The second-order differential equation describing the behavior of the zeroth-order boundary function is investigated using the dual operator formalism — an analog of the conjugate operator in the linear theory. The application of this formalism has produced an asymptotic solution and has also made it possible to propose a number of homogeneous discrete three-point schemes for solving the equation.


Asymptotic Solution Asymptotic Expression Dual Operator Conjugate Operator Singular Perturbation Theory 


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© Springer Science+Business Media, Inc. 2006

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  • D. S. Filippychev

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