Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A FIFTH ORDER NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH NEGATIVE SHIFT

  • Chakravarthy, P. Pramod (Department of Mathematics, Visvesvaraya National Institute of Technology) ;
  • Phaneendra, K. (Department of Mathematics, Kakatiya Institute of Technology & Science) ;
  • Reddy, Y.N. (Department of Mathematics at National Institute of Technology)
  • Published : 2009.01.31
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Abstract

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

Keywords

References

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