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Local meshless differential quadrature collocation method for time-fractional PDEs. (English) Zbl 1451.65166

Summary: This paper is concerned with the numerical solution of time-fractional partial differential equations (PDEs) via local meshless differential quadrature collocation method (LMM) using radial basis functions (RBFs). For the sake of comparison, global version of the meshless method is also considered. The meshless methods do not need mesh and approximate solution on scattered and uniform nodes in the domain. The local and global meshless procedures are used for spatial discretization. Caputo derivative is used in the temporal direction for both the values of \( \alpha \in (0,1) \) and \( \alpha\in(1,2) \). To circumvent spurious oscillation caused by convection, an upwind technique is coupled with the LMM. Numerical analysis is given to asses accuracy of the proposed meshless method for one- and two-dimensional problems on rectangular and non-rectangular domains.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
35R11 Fractional partial differential equations
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