Meshless method with ridge basis functions for time fractional two-flow domain model

Abstract

In this paper, a meshless method with ridge basis functions for solving the time fractional two-flow domain model problem is proposed. The method uses the L1 approximation formula based on piecewise linear interpolation to discretize the Caputo time fractional derivative \( (0 < \alpha < 1) \), and by means of the ridge basis function to construct the approximation function, and uses the collocation method to discretize the governing equation. The existence and uniqueness of the numerical solution are analyzed. The error between the proposed method and the finite difference method is compared by numerical examples; then the affecting factors of the calculation accuracy are discussed. The results show that the proposed method is feasible and simple.

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Correspondence to Xinqiang Qin.

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Qin, X., Li, K. & Hu, G. Meshless method with ridge basis functions for time fractional two-flow domain model. Math Sci (2020). https://doi.org/10.1007/s40096-020-00348-3

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Keywords

  • Time fractional two-flow domain model
  • Caputo derivative
  • Ridge basis functions
  • Meshless method
  • Collocation method