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Solving the forward-backward heat equation in two-dimension by Radial basis functions mesh free method

 Siamak Banei1*, Kamal Shanazari1, Yaqub Azari2, and Yones Esmaeelzade Aghdam2

1Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran

2Faculty of Science, Shahid Rajaee Teacher Training University, Lavizan, Tehran, 16785-163

*Corresponding author’s e-mail: [email protected] 

Original: 21 February 2020        Revised: 18 August 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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This study is specially designed to solve the forward-backward heat equation in two dimension to make use of thin plate splines and finite difference method. It should be noted that the problem had more than one part categorization. The results as a whole covered a large proportion solutions by a radial basis function method for spatial and finite difference scheme along with interface boundry usage . This method was presented based on updating interface boundry. In addition , the interpolation and the collcation methods have supported through using of thin plate splines and finite difference method to update interface boundary. Furthermore, it showed that the time dicretization scheme was unconditionally stable and convergent. . Finally, some numerical examples were assigned to graded methods to support their efficiency.

Key Words: Radial basis functions, Meshless method, Thin plate spline, Domain decomposition, Finite difference