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Higher order Chebyshev basis functions for two‐point boundary value problems
Author(s) -
Bamigbola O. M.,
Ibiejugba M. A.,
Onumanyi P.
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260203
Subject(s) - mathematics , basis function , chebyshev polynomials , basis (linear algebra) , galerkin method , boundary value problem , mathematical analysis , chebyshev filter , chebyshev nodes , finite element method , geometry , physics , thermodynamics
Cubic basis functions in one dimension for the solution of two‐point boundary value problems are constructed based on the zeros of Chebyshev polynomials of the first kind. A general formula is derived for the construction of polynomial basis functions of degree r , where 1 ≤ r < ∞. A Galerkin finite element method using the constructed basis functions for the cases r = 1, 2 and 3 is successfully applied to three different types of problem including a singular perturbation problem.