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

Arshad Hussain | Zendy; Marjan Uddin | Zendy; Sirajul Haq | Zendy; Hameed Ullah Jan | Zendy

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

Author(s) -

Arshad Hussain,

Marjan Uddin,

Sirajul Haq,

Hameed Ullah Jan

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/8862139

Subject(s) - polar coordinate system , radial basis function , meshfree methods , cylindrical coordinate system , discretization , partial differential equation , polar , bipolar coordinates , mathematical analysis , method of lines , work (physics) , spherical coordinate system , basis function , parabolic cylindrical coordinates , basis (linear algebra) , mathematics , log polar coordinates , generalized coordinates , ordinary differential equation , differential equation , parabolic partial differential equation , computer science , geometry , physics , finite element method , thermodynamics , differential algebraic equation , astronomy , machine learning , parabolic cylinder function , artificial neural network

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.

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