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New Fifth-Kind Chebyshev Collocation Scheme for First-Order Hyperbolic and Second-Order Convection-Diffusion Partial Differential Equations

Author

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  • Mahmoud M. Mokhtar
  • M. H. El Dewaik
  • Waleed Adel

Abstract

The fifth type of Chebyshev polynomials was used in tandem with the spectral tau method to achieve a semianalytical solution for the partial differential equation of the hyperbolic first order. For this purpose, the problem was diminished to the solution of a set of algebraic equations in unspecified expansion coefficients. The convergence and error analysis of the proposed expansion were studied in-depth. Numerical trials have confirmed the applicability and the accuracy.

Suggested Citation

  • Mahmoud M. Mokhtar & M. H. El Dewaik & Waleed Adel, 2022. "New Fifth-Kind Chebyshev Collocation Scheme for First-Order Hyperbolic and Second-Order Convection-Diffusion Partial Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, October.
    • Handle: RePEc:hin:jnlmpe:3789611
    DOI: 10.1155/2022/3789611
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