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Improved singular boundary method and dual reciprocity method for fractional derivative Rayleigh–Stokes problem

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Abstract

The improved singular boundary method (ISBM) and dual reciprocity method (DRM) are coupled to solve fractional derivative the Rayleigh–Stokes problem with nonhomogeneous term. This method is free of mesh and integration, mathematically simple, and easy to program. Also, origin intensity factors (OIFs) significant techniques in ISBM make the method as a strong meshless method. First, the time-fractional derivative term in mentioned equation is discretized; then, ISBM–DRM is utilized to solve consequent equation. It is proved the method is unconditionally stable and convergent with convergence order \({\mathcal {O}}(\tau ^{1+\alpha })\). In addition, numerical results confirm the accuracy and efficiency of the presented scheme.

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Acknowledgements

The work in this paper is supported by the National Natural Science Foundation of China (Nos. 11772121, 11702083, 11572112) and the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) (No. MCMS-0218G01).

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  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, International Center for Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

    Farzaneh Safari & HongGuang Sun

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Safari, F., Sun, H. Improved singular boundary method and dual reciprocity method for fractional derivative Rayleigh–Stokes problem. Engineering with Computers 37, 3151–3166 (2021). https://doi.org/10.1007/s00366-020-00991-3

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