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https://doi.org/10.1109/EuMIC.2016.7777565

has been cited by the following article:

• TITLE: Chebyshev Polynomial-Based Analytic Solution Algorithm with Efficiency, Stability and Sensitivity for Classic Vibrational Constant Coefficient Homogeneous IVPs with Derivative Orders n, n-1, n-2

  AUTHORS: David P. Stapleton

  KEYWORDS: Differential Equation, Stability, Sensitivity Analysis, Chebyshev Polynomials, Coefficient Formula

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.12 No.4, October 19, 2022

  ABSTRACT: The Chebyshev polynomials are harnessed as functions of the one parameter of the nondimensionalized differential equation for trinomial homogeneous linear differential equations of arbitrary order n that have constant coefficients and exhibit vibration. The use of the Chebyshev polynomials allows calculation of the analytic solutions for arbitrary n in terms of the orthogonal Chebyshev polynomials to provide a more stable solution form and natural sensitivity analysis in terms of one parameter and the initial conditions in 6n + 7 arithmetic operations and one square root.