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 ()
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.
Share and Cite:
Stapleton, D. (2022) 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.
American Journal of Computational Mathematics,
12, 331-340. doi:
10.4236/ajcm.2022.124023.
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