An accurate computational method for two-dimensional (2D) fractional Rayleigh-Stokes problem for a heated generalized second grade fluid via linear barycentric interpolation method. (15th July 2022) - Oruç, Ömer
Highlights: Two-dimensional fractional Rayleigh-Stokes problem is investigated. A reliable linear barycentric interpolation method is developed for Rayleigh-Stokes problem. Very accurate results are obtained. Abstract: This paper deals with the development and analysis of an efficient method for the numerical solution of the two-dimensional (2D) fractional Rayleigh-Stokes problem for a heated generalized second grade fluid. The fractional time derivative that occurs in the problem is in the Riemann-Liouville sense and is discretized using a finite difference approach that is convergent with order of convergence O ( τ 1 + β ) and unconditionally stable. After discretization of time variable, linear barycentric interpolation method is used to discretize space variables. In this way, a fully discrete scheme is obtained, which can be used to solve the problem numerically. The numerical solution is compared with exact solution to see how accurate it is. Also L ∞ error norm is reckoned and compared with those of other numerical methods in the literature to see performance of the method. Numerical simulations verify that the suggested method is accurate and workable for similar 2D fractional problems.