Some numerical experiments on singularly perturbed problems with multi-parameters

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SOME NUMERICAL EXPERIMENTS ON SINGULARLY PERTURBED PROBLEMS

WITH MULTI-PARAMETERS

Conference Paper · August 2019

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8th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2019), August 27-30, 2019, Baku, Azerbaijan

SOME NUMERICAL EXPERIMENTS ON SINGULARLY PERTURBED

PROBLEMS WITH MULTI-PARAMETERS

S¨

uleyman Cengizci

1

Abstract. In this study, numerical behavior of singular perturbed ordinary differential equa-tions that depend on positive small parameters is investigated. An efficient method that com-bines the well-known Finite Element Method (FEM) and an asymptotic approach so-called Successive Complementary Expansion Method (SCEM) is employed for numerical simulations of the multi-parameter problems.

Keyword: Asymptotic approximation, singular perturbation, finite element method, multi-parameter problem, SCEM.

AMS 2010: 34E15, 65L11, 65L60.

References

[1] Logg, Anders, Kent-Andre Mardal, and Garth Wells, eds. Automated solution of differential equations by the finite element method: The FEniCS book. Vol. 84. Springer Science & Business Media, 2012.

[2] Cousteix, Jean, and Jacques Mauss. Asymptotic analysis and boundary layers. Springer Science & Business Media, 2007.

[3] Larson, Mats G., and Fredrik Bengzon. The finite element method: theory, implementation, and applications. Vol. 10. Springer Science & Business Media, 2013.

[4] Lin, Torsten, and Hans-Grg Roos. ”Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters.” Journal of Mathematical Analysis and Applications 289.2 (2004): 355-366. [5] Natesan, S., J. L. Gracia, and C. Clavero. ”Singularly perturbed boundary-value problems with two small

parameters-a defect correction approach.” Proceedings of the International Conference on Boundary and Interior LayersComputational and Asymptotic Methods, BAIL. 2004.

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