Analysis of the numerical scheme of the one-dimensional fractional Rayleigh–Stokes model arising in a heated generalized problem
Source abstract
Abstract
In this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using the construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation to estimate the time derivative. Therefore, we design an authentic and fast numerical calculation approach based on the elaborated convergence rate recovery method. The matrix of the derivative operation of an orthogonal GBP is gained by employing the characteristic of this type of polynomial. The privilege of the numerical method is the orthogonality of the GBP and operational matrices, which reduces time computation and increases speed. Eventually, we propose three numerical examples to check the validity and numerical studies to illustrate the precision and efficiency of the new approach.
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Research context
OpenAlex topics: Fractional Differential Equations Solutions · Differential Equations and Numerical Methods · Numerical methods in engineering
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Affiliations
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University 1 , Tehran 16785 -136, I. R. Iran
Department of Mathematics, Faculty of Science, Qom University of Technology 2 , Qom, I. R. Iran
References (29)
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