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Cubic quasi-interpolation spline collocation method for solving convection–diffusion equations

Author

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  • Bouhiri, S.
  • Lamnii, A.
  • Lamnii, M.

Abstract

In this paper, we use a cubic spline collocation method to solve a two dimensional convection–diffusion equation. More precisely, we approximate first and second order partial derivatives by those of cubic spline quasi-interpolants to produce a system of first order ordinary differential equations. The resulting system can be solved using MATLAB’s ode solver. Error estimates of quasi-interpolants which are used are given with full discussion. Furthermore, numerical examples are presented to show the validity of our methods.

Suggested Citation

  • Bouhiri, S. & Lamnii, A. & Lamnii, M., 2019. "Cubic quasi-interpolation spline collocation method for solving convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 33-45.
    • Handle: RePEc:eee:matcom:v:164:y:2019:i:c:p:33-45
    DOI: 10.1016/j.matcom.2018.11.003
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    References listed on IDEAS

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    1. Serghini, A. & Tijini, A., 2015. "Construction of univariate spline quasi-interpolants with symmetric functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 329-342.
    2. Foucher, Françoise & Sablonnière, Paul, 2009. "Quadratic spline quasi-interpolants and collocation methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3455-3465.
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