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Direct meshless local Petrov-Galerkin (DMLPG) method for time-fractional fourth-order reaction-diffusion problem on complex domains. (English) Zbl 1443.65188
Summary: A new numerical scheme has been developed based on the fast and efficient meshless local weak form i.e direct meshless local Petrov-Galerkin (DMLPG) method for solving the fractional fourth-order partial differential equation on computational domains with complex shape. The fractional derivative is the Riemann-Liouville fractional derivative. At first, a finite difference scheme with the second-order accuracy has been employed to discrete the time variable. Then, the DMLPG technique is employed to achieve a full-discrete scheme. The time-discrete scheme has been studied in terms of unconditional stability and convergence order by the energy method in the \(L^2\) space. Also, some numerical results are presented to show the efficiency and accuracy of the proposed technique on the simple and complex domains with the irregular and non-regular grid points.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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