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Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

Author

Listed:
  • Jen-Yi Chang

    (General Education Center, Tainan University of Technology, Tainan 71002, Taiwan)

  • Ru-Yun Chen

    (Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

  • Chia-Cheng Tsai

    (Bachelor Degree Program in Ocean Engineering and Technology, National Taiwan Ocean University, Keelung 202301, Taiwan
    Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

Abstract

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Suggested Citation

  • Jen-Yi Chang & Ru-Yun Chen & Chia-Cheng Tsai, 2022. "Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems," Mathematics, MDPI, vol. 10(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:188-:d:720089
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    References listed on IDEAS

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    1. Arafat Hussain & Zhoushun Zheng & Eyaya Fekadie Anley, 2020. "Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method," Mathematics, MDPI, vol. 8(11), pages 1-21, October.
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