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

  • Hadi Roohani GhehsarehEmail author
  • Marzie Raei
  • Ali Zaghian
Technical Paper


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.


Meshless local radial point interpolation method Two-dimensional fractional Tricomi-type equation Weak formulation Radial basis functions Stability analysis 



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


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsMalek Ashtar University of TechnologyShahin ShahrIran

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