RBFs approximation method for time fractional partial differential equations |
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| Institution: | 1. Department of Mathematics, Shiraz University of Technology, Shiraz, Iran;2. School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China;3. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, Jiangsu, PR China;2. Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, Jiangsu, PR China |
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| Abstract: | In this paper, radial basis functions (RBFs) approximation method is implemented for time fractional advection–diffusion equation on a bounded domain. In this method the first order time derivative is replaced by the Caputo fractional derivative of order α ∈ (0, 1], and spatial derivatives are approximated by the derivative of interpolation in the Kansa method. Stability and convergence of the method is discussed. Several numerical examples are include to demonstrate effectiveness and accuracy of the method. |
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