DOI: 10.15672/hujms.1764558 ISSN: 2651-477X

A local meshfree method based on radial basis function partition of unity method for two-dimensional (2D) fractional Rayleigh-Stokes problem

Ömer Oruç
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This study dedicated to provide numerical solutions of fractionalRayleigh-Stokes problem in two-dimension (2D). The problem has Riemann-Liouvilletype fractional derivative. To obtain time discretization for theconsidered problem, we use a difference scheme along with an integrationprocedure. Hence a time semi-discretized scheme is obtained. We examinestability and convergence of the time semi-discretized scheme. Thenwe developed a local radial basis function partition of unity methodfor discretization of space variables. By combining time and spacediscretization we acquire a full discrete scheme for solving the consideredproblem. We solve some test problems and compare obtained resultsfor the test problems with existing techniques in the literature,to show efficiency of the proposed method.

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