Numerical solution of two-point boundary value problems using

  • Authors:

  • Kenzu Abdella

  • Affiliations:

  • Qatar University, Department of Mathematics, Statistics and Physics, Doha, Qatar

  • Venue:
  • AMERICAN-MATH'12/CEA'12 Proceedings of the 6th WSEAS international conference on Computer Engineering and Applications, and Proceedings of the 2012 American conference on Applied Mathematics
  • Year:
  • 2012

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Abstract

This paper presents the application of Sinc method to solve second order two-point boundary value problems based on derivative interpolation. Even in the presence of singularities, the Sinc numerical method is known to exhibit exponential convergence, resulting in highly accurate solutions. However, the customary approach of interpolating the solution variable with the Sinc bases requires first and higher order differentiations which induce high sensitivity to numerical errors. In contrast, in this paper, we use first derivative interpolation whose integration is much less sensitive to numerical errors. Moreover, derivative conditions at boundaries are treated with appropriate transformations in order to prevent numerical overflows near boundaries. Unlike previous approaches, the current approach preserves the exponential convergence associated with the Sinc numerical methods.