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Application of Sinc-Galerkin method to singularly perturbed parabolic convection-diffusion problems

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Abstract

We develop a numerical algorithm for solving singularly perturbed one-dimensional parabolic convection-diffusion problems. The method comprises a standard finite difference to discretize in temporal direction and Sinc-Galerkin method in spatial direction. The convergence analysis and stability of proposed method are discussed in details, it is justifying that the approximate solution converges to the exact solution at an exponential rate. we know that the conventional methods for these problems suffer due to decreasing of perturbation parameter, but the Sinc method handel such difficulty as singularity. This scheme applied on some test examples, the numerical results illustrate the efficiency of the method and confirm the theoretical behavior of the rates of convergence.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Hengam, Narmak, Tehran, Iran

    J. Rashidinia, A. Barati & M. Nabati

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  1. J. Rashidinia
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  2. A. Barati
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  3. M. Nabati
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Correspondence to J. Rashidinia.

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Rashidinia, J., Barati, A. & Nabati, M. Application of Sinc-Galerkin method to singularly perturbed parabolic convection-diffusion problems. Numer Algor 66, 643–662 (2014). https://doi.org/10.1007/s11075-013-9752-5

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  • DOI: https://doi.org/10.1007/s11075-013-9752-5

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