Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model

Mohammed M. Al-Shomrani, Mohamed A. Abdelkawy and António M. Lopes ()
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Mohammed M. Al-Shomrani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21577, Saudi Arabia
Mohamed A. Abdelkawy: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi Arabia
António M. Lopes: Associated Laboratory for Energy, Transport and Aeronautics/Institute of Science and Innovation in Mechanical Engineering and Industrial Engineering (LAETA/INEGI), Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: Applications of non-Newtonian fluids have been widespread across industries, accompanied by theoretical developments in engineering and mathematics. This paper studies a two-dimensional multi-term time fractional viscoelastic non-Newtonian fluid model by using two autonomous consecutive spectral collocation strategies. A modification of the spectral approach is implemented, leading to an algebraic system of equations able to obtain an approximate symmetric solution for the model. Numerical examples illustrate the effectiveness of the technique in terms of accuracy and convergence.

Keywords: time fractional non-Newtonian fluid model; collocation method; spectral method; Gauss-type quadrature; modern technologies (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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