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Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines

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  • Arshad Hussain
  • Marjan Uddin
  • Sirajul Haq
  • Hameed Ullah Jan
  • Fazlollah Soleymani

Abstract

We propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial basis functions (RBFs), much of the research are devoted to the partial differential equations in rectangular coordinates. This work is an attempt to explore the versatility of RBFs in nonrectangular coordinates as well. The results show that application of RBFs is equally good in polar cylindrical coordinates. Comparison with other cited works confirms that the present approach is accurate as well as easy to implement to problems in higher dimensions.

Suggested Citation

  • Arshad Hussain & Marjan Uddin & Sirajul Haq & Hameed Ullah Jan & Fazlollah Soleymani, 2021. "Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, December.
    • Handle: RePEc:hin:jjmath:8862139
    DOI: 10.1155/2021/8862139
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    Cited by:

    1. Hussain, Manzoor & Ghafoor, Abdul & Hussain, Arshad & Haq, Sirajul & Ali, Ihteram & Arifeen, Shams Ul, 2024. "A hybrid kernel-based meshless method for numerical approximation of multidimensional Fisher’s equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 130-157.

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