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2013•Journal of Anhui Normal UniversityRequires access

The Asymptotic Solution of a Class of Nonlinear Singularly Perturbed Problems

Cheng Ouyang

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Abstract

Using the matching asymptotic expansion method,a class of nonlinear singularly perturbed boundary value problems on an infinite long region is studied,and the uniformly valid asymptotic expansion with the first order for the solution is given.First solving the outer expansion,and then solving interior expansion with the contraction transformation.Using the generalized integral and Taylor expansion,the internal expansion and the outer one are matched,and the uniformly valid compound expansion is obtained.Through studying this class of new nonlinear problems on the infinite long region,the studied range of the similar problems is expanded.And it is provided with a reference for the research on the related singularly perturbed problems.

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What this paper is about

Using the matching asymptotic expansion method,a class of nonlinear singularly perturbed boundary value problems on an infinite long region is studied,and the uniformly valid asymptotic expansion with the first order for the solution is given.First solving the outer expansion,and then solving interior expansion with the contraction transformation.Using the generalized integral and Taylor expansion,the internal expansion and the outer one are matched,and the uniformly valid compound expansion is obtained.Through studying this class of new nonlinear problems on the infinite long region,the studied range of the similar problems is expanded.And it is provided with a reference for the research on the related singularly perturbed problems.

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Available abstract

Using the matching asymptotic expansion method,a class of nonlinear singularly perturbed boundary value problems on an infinite long region is studied,and the uniformly valid asymptotic expansion with the first order for the solution is given.First solving the outer expansion,and then solving interior expansion with the contraction transformation.Using the generalized integral and Taylor expansion,the internal expansion and the outer one are matched,and the uniformly valid compound expansion is obtained.Through studying this class of new nonlinear problems on the infinite long region,the studied range of the similar problems is expanded.And it is provided with a reference for the research on the related singularly perturbed problems.

Key concepts: Method of matched asymptotic expansions, Asymptotic expansion, Mathematics, Nonlinear system, Taylor series, Singular perturbation, Mathematical analysis, Class (philosophy)

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