W. M. Abd-Elhameed1,2,*, Asmaa M. Alkenedri2
CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603
Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for
the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi
polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely,
Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based
on making use of the power series representations and inversion formulas of these classes of polynomials. The
derived formulas serve in converting the even-order… More >
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