JAMC

Article http://dx.doi.org/10.26855/jamc.2020.12.010

Improved High Order Methods Using Boundary Layer Detection for a Singular Perturbation Problem

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Weiqun Zhang

Department of Mathematics, Wright State University, Lake Campus, Ohio, USA.

*Corresponding author: Weiqun Zhang

Published: December 11,2020

Abstract

A singular perturbation problem is solved with improved high order methods using boundary layer detection theorems. The stability and convergence, independent of the singular perturbation parameter, is numerically verified.

References

[1] K. W. Chang and F. A. Howes. (1984). Nonlinear Singular Perturbation Phenomena: Theory and Application. Spring-Verlag.

[2] R. E. O’Malley Jr. (1974). Introduction to Singular Perturbations. Academic Press, New York.

[3] J. J. H. Miller, E. O’Riordan, G. I. Shishkin. (1996). Fitted numerical methods for singular perturbation problems. World Scientific.

[4] W. Zhang, D. H. Schultz, and Lin. (2008). Numerical Solutions of Linear and Nonlinear Singular Perturbation Problems. Computers & Math. Applic., Vol. 55, Issue 11, June 2008, pp. 2574-2592.

[5] H. B. Keller. (1968). Numerical Methods for Two-Point Boundary Value Problems. Blaisdell Publishing Company.

[6] S. R. Choudhury. (1996). Nonstandard Difference Schemes of Nonlinear Singular Perturbation Problems. Int. J. of Applied Sc. & Computations, Vol. 2, pp. 375-392, February 1996.

[7] F. O. Ilicasu and D. H. Schultz. (2002). High Order Methods for Singular Perturbation Problems. Computers Math. Applic., Vol. 47, pp. 391-417.

[8] P. D. Lax and A. N. Milgram. (n.d.). Contributions to the Theory of Partial Differential Equations. Annals of Ma-thematics Studies, Princeton University Press.

[9] W. Zhang. (2019). A Uniformly Convergent Numerical Method Using Weak Formulation for Singularly Perturbed Differential Equations. Journal of Mathematics and System Science, Vol. 9, No. 1, pp. 1-6, doi: 10.17265/2159-5291.

How to cite this paper

Improved High Order Methods Using Boundary Layer Detection for a Singular Perturbation Problem

How to cite this paper: Weiqun Zhang. (2020) Improved High Order Methods Using Boundary Layer Detection for a Singular Perturbation Problem. Journal of Applied Mathematics and Computation, 4(4), 189-194.

DOI: http://dx.doi.org/10.26855/jamc.2020.12.010