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Application of Pell collocation method for solving the general form of time-fractional Burgers equations

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Abstract

This paper provides a fruitful and effective spectral scheme based on the two-dimensional Pell collocation method for treating of nonlinear time-fractional Burgers equations with variable coefficients. The fractional Burgers equation is a beneficial model for describing the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. In order to provide a numerical scheme, we consider the two-dimensional Pell polynomials and estimate the Caputo fractional derivative as well as other terms in the main equation by operational matrices. By collocating resultant approximate equations and initial-boundary conditions, a nonlinear system of equations arises, which can be solved via \(\texttt {fsolve}\) command in MATLAB. The convergence of the numerical scheme is fully discussed. Several test problems are presented for comparing our results with other numerical methods in the literature.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    M. Taghipour & H. Aminikhah

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O. Box 1914, Rasht, 41938, Iran

    H. Aminikhah

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  1. M. Taghipour
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  2. H. Aminikhah
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Taghipour, M., Aminikhah, H. Application of Pell collocation method for solving the general form of time-fractional Burgers equations. Math Sci 17, 183–201 (2023). https://doi.org/10.1007/s40096-021-00452-y

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