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A meshless method to solve the variable-order fractional diffusion problems with fourth-order derivative term
  • Farzaneh Safari,
  • Jing Li
Farzaneh Safari
Changsha University of Science and Technology

Corresponding Author:[email protected]

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Jing Li
School of Mathematical Science and Computing Technology
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Abstract

Using the meshless collocation method, a scheme for solving nonlinear variable-order fractional diffusion equation with fourth-order derivative term is presented. Here approximations to fractional derivative term are obtained by weighted and shifted Gr\”unwald difference (WSGD) approximation formula. The difficulty caused by the nonlinear terms is carefully handled by quasilinearization technique. Using the radial basis functions, the solution of the problem is written in terms of the primary approximation, and the related correcting functions at each time step. Then the approximation is substituted back to the governing equations where the unknown parameters can be determined. Finally, the method is supported by several numerical experiment on irregular domains.