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Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem

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Abstract

The paper is devoted to investigate the two-dimensional time-fractional Tricomi-type equation, which describes the anomalous process of nearly sonic speed gas dynamics. An efficient numerical process, based on the combination of time stepping method and meshless local weak formulation, is performed to solve the model. Firstly, an implicit finite difference scheme is used to discrete the problem in time direction. The unconditional stability of the proposed time discretization scheme is proven. Then, a meshfree method based on the combination of local Petrov–Galerkin formulation and strong form is implemented to fully discretize the underlying problem. In our implementation, the radial point interpolation basis functions and local Heaviside step functions are used as the basis and test functions, respectively. A simple collocation process is employed to impose the Dirichlet boundary conditions directly. Finally, two numerical experiments on regular and irregular domains are presented to verify the efficiency, validity and accuracy of the technique.

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Acknowledgements

The authors would like to express their thankfulness to anonymous referees for their helpful constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, Malek Ashtar University of Technology, Shahin Shahr, Isfahan, 83145-115, Iran

    Hadi Roohani Ghehsareh, Marzie Raei & Ali Zaghian

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  1. Hadi Roohani Ghehsareh
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  2. Marzie Raei
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  3. Ali Zaghian
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Correspondence to Hadi Roohani Ghehsareh.

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Ghehsareh, H.R., Raei, M. & Zaghian, A. Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem. J Braz. Soc. Mech. Sci. Eng. 41, 252 (2019). https://doi.org/10.1007/s40430-019-1749-0

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