A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters

ZHU Hongbao; CHEN Songlin

doi:10.21656/1000-0887.410082

Volume 41 Issue 11

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ZHU Hongbao, CHEN Songlin. A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters[J]. Applied Mathematics and Mechanics, 2020, 41(11): 1292-1296. doi: 10.21656/1000-0887.410082

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A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters

doi: 10.21656/1000-0887.410082

School of Mathematics & Physics, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China

Received Date: 2020-03-17
Rev Recd Date: 2020-04-17
Publish Date: 2020-11-01

Abstract

Abstract

A class of 2nd-order singularly perturbed time delay nonlinear problems were considered. The asymptotic solution to the problem was obtained with the singular perturbation method. Firstly, The outer solution was constructed by means of the singular perturbation method. Then, a stretched variable was introduced, the boundary layer correction of the solution was obtained, and the asymptotic analytic expansion solution to the problem was also given. Finally, under suitable conditions, the theory of differential inequalities was applied to prove the uniformly valid asymptotic expansion of the solution to the original problem.
- nonlinear,
- singularly perturbed,
- 2 parameters,
- time delay

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References(12)

References

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