An efficient meshless method based on RBFs for the time fractional diffusion-wave equation
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This paper proposes a numerical method to deal with time-fractional diffusion-wave equation (one-dimensional and two-dimensional). The time-fractional term of the problem is scheduled in Caputo sense which is popular in analyzing time-fractional dependent problems. The proposed technique is based on radial basis functions and more, it is a kind of meshless method, therefore it is not difficult applying the method to handle two or three dimensional time-fractional diffusion-wave problems especially when the domain are more general and not regular forms. The generalized thin plate splines (GTPS) radial basis functions are employed. Numerical examples are given to test the accuracy. Three numerical experiments reveal that proposed method is very convenient for solving such problems.
KeywordsRadial basis function Fractional PDE Diffusion-wave equation Kansa’s method Finite differences \(\theta \)-method
Mathematics Subject Classifcation65M06 65N12 26A33
- 10.Ahmadian, A., Ismail, F., Salahshour, S., Baleanu, D., Ghaemi, F.: Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution. Commun. Nonlinear Sci. Numer. Simul. 53, 44–64 (2017). https://doi.org/10.1016/j.cnsns.2017.03.012 MathSciNetCrossRefGoogle Scholar
- 17.Liu, G., Gu, Y.: An introduction to meshfree methods and their programing. Springer, New York (2005)Google Scholar
- 24.Melenk, J.M., Babǔska, I.: The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Engrg. 139, 289–314 (1996)Google Scholar