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More accurate results for two-dimensional heat equation with Neumann’s and non-classical boundary conditions

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Abstract

In this article, recently proposed spectral meshless radial point interpolation (SMRPI) method is applied to the two-dimensional diffusion equation with a mixed group of Dirichlet’s and Neumann’s and non-classical boundary conditions. The present method is based on meshless methods and benefits from spectral collocation ideas. The point interpolation method with the help of radial basis functions is proposed to construct shape functions which have Kronecker delta function property. Evaluation of high-order derivatives is possible by constructing and using operational matrices. The computational cost of the method is modest due to using strong form equation and collocation approach. A comparison study of the efficiency and accuracy of the present method and other meshless methods is given by applying on mentioned diffusion equation. Stability and convergence of this meshless approach are discussed and theoretically proven. Convergence studies in the numerical examples show that SMRPI method possesses excellent rates of convergence.

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Acknowledgments

The author is very grateful to two anonymous reviewers for carefully reading the paper and for their comments and suggestions which have improved the paper very much.

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  1. Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran

    Elyas Shivanian

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Shivanian, E. More accurate results for two-dimensional heat equation with Neumann’s and non-classical boundary conditions. Engineering with Computers 32, 729–743 (2016). https://doi.org/10.1007/s00366-016-0449-y

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