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Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems

    Saeid Abbasbandy Affiliation
    ; Hussein Sahihi Affiliation
    ; Tofigh Allahviranloo Affiliation
DOI:

Abstract

In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.

Keyword : reproducing kernel method, singularly perturbed parabolic problems, error analysis, boundary layer behavior

How to Cite
Abbasbandy, S., Sahihi, H., & Allahviranloo, T. (2021). Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems. Mathematical Modelling and Analysis, 26(1), 116-134. http://doi.org/10.3846/mma.2021.12057
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Jan 18, 2021
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