Nonlinear Engineering (Aug 2023)

Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation

  • Moustafa Mohamed,
  • Youssri Youssri Hassan,
  • Atta Ahmed Gamal

DOI
https://doi.org/10.1515/nleng-2022-0308
Journal volume & issue
Vol. 12, no. 1
pp. 5652 – 61

Abstract

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In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The L∞{L}_{\infty } and L2{L}_{2} norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm.

Keywords