Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE METHOD OF ASYMPTOTIC INNER BOUNDARY CONDITION FOR SINGULAR PERTURBATION PROBLEMS

  • Andargie, Awoke (Department of Mathematics, Bahir dar University) ;
  • Reddy, Y.N. (Department of Mathematics, National Institute of Technology)
  • Received : 2010.04.24
  • Accepted : 2010.11.25
  • Published : 2011.05.30
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Abstract

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

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References

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