Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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UNIFORMLY CONVERGENT NUMERICAL SCHEME FOR A SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS ARISING IN COMPUTATIONAL NEUROSCIENCE

  • 투고 : 2020.08.15
  • 심사 : 2021.05.04
  • 발행 : 2021.09.30
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초록

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

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과제정보

The authors would like to thank the anonymous referees for their helpful comments that improved the quality of this paper.

참고문헌

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