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2012•Journal of Hunan Institute of EngineeringRequires access

A Class of Singularly Perturbed Boundanry Value Problems for Fourth-order Nonlinear Equation

Keng Cheng Ang

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Abstract

Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems for forth-order nonlinear equation is studied.Firstly,the outer solution with four arbitrary constants of the problem is solved;secondly,introducing the stretched variables,according to the boundary conditions and the matching rule,the outer solution and the interior solutions near the left and right boundary layers are determined.Finally,the asymptotic solution of the problem is obtained.

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What this paper is about

Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems for forth-order nonlinear equation is studied.Firstly,the outer solution with four arbitrary constants of the problem is solved;secondly,introducing the stretched variables,according to the boundary conditions and the matching rule,the outer solution and the interior solutions near the left and right boundary layers are determined.Finally,the asymptotic solution of the problem is obtained.

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Available abstract

Using the matching asymptotic expansion method,a class of singularly perturbed boundary value problems for forth-order nonlinear equation is studied.Firstly,the outer solution with four arbitrary constants of the problem is solved;secondly,introducing the stretched variables,according to the boundary conditions and the matching rule,the outer solution and the interior solutions near the left and right boundary layers are determined.Finally,the asymptotic solution of the problem is obtained.

Key concepts: Method of matched asymptotic expansions, Mathematics, Nonlinear system, Boundary value problem, Class (philosophy), Mathematical analysis, Singular perturbation, Matching (statistics)

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