10.1007/s40096-021-00452-y

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

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  • M. Taghipour1,
  • H. Aminikhah*2,
  1. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, 41938, IR
  2. Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, 41938, IR Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, 41938, IR

Published in Issue 2022-01-07

How to Cite

Taghipour, M., & Aminikhah, H. (2022). Application of Pell collocation method for solving the general form of time-fractional Burgers equations. Mathematical Sciences, 17(2 (June 2023). https://doi.org/10.1007/s40096-021-00452-y
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Abstract

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 fsolve\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {fsolve}$$\end{document} 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.

Keywords

  • Nonlinear time-fractional Burgers equation,
  • Pell polynomials,
  • Spectral collocation method,
  • Caputo fractional derivative,
  • Convergence analysis

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