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A Modified RBF Collocation Method for Solving the Convection‐Diffusion Problems

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  • Nissaya Chuathong

Abstract

The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection‐diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results.

Suggested Citation

  • Nissaya Chuathong, 2023. "A Modified RBF Collocation Method for Solving the Convection‐Diffusion Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlaaa:v:2023:y:2023:i:1:n:8727963
    DOI: 10.1155/2023/8727963
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    References listed on IDEAS

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    1. Lee Ken Yap & Fudziah Ismail & Norazak Senu, 2014. "An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
    2. Lee Ken Yap & Fudziah Ismail & Norazak Senu, 2014. "An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. 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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