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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2014, 19(3), 208-217; https://doi.org/10.3390/mca19030208

# Special Finite Difference Method for Singular Perturbation Problems with One-End Boundary Layer

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Department of Mathematics, Nizam College, Osmania University, 500001 Hyderabad, India
2
Department of Mathematics, National Institute of Technology, Warangal-506004, India
*
Authors to whom correspondence should be addressed.
Published: 1 December 2014
PDF [264 KB, uploaded 4 March 2016]

# Abstract

In this paper, we have presented a special finite difference method for solving a singular perturbation problem with layer behaviour at one end. In this method, we have used a second order finite difference approximation for the second derivative, a modified second order upwind finite difference approximation for the first derivative and a second order average difference approximation for y to reduce the global error and retaining tridiagonal system. Then the discrete invariant imbedding algorithm is used to solve the tridiagonal system. This method controls the rapid changes that occur in the boundary layer region and it gives good results in both cases i.e., h ≤ ε and ε << h. The existence and uniqueness of the discrete problem along with stability estimates are discussed. Also we have discussed the convergence of the method. We have presented maximum absolute errors for the standard examples chosen from the literature.
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

MDPI and ACS Style

Phaneendra, K.; Madhulatha, K.; Reddy, Y. Special Finite Difference Method for Singular Perturbation Problems with One-End Boundary Layer. Math. Comput. Appl. 2014, 19, 208-217.

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