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

Taghipour M.; Aminikhah H.

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

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摘要

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 fslove 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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《mathematical sciences》 |2023年第2期|183-201|共19页
作者
Taghipour M.; Aminikhah H.;
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Univ Guilan;

Univ Guilan;

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正文语种英语
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Nonlinear time-fractional Burgers equation; Pell polynomials; Spectral collocation method; Caputo fractional derivative; Convergence analysis; CONVECTION-DIFFUSION EQUATIONS;

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

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