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A Modified Shifted Gegenbauer Polynomials for the Numerical Treatment of Second-Order BVPs |
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PP: 1-12 |
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doi:10.18576/msl/110101
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Author(s) |
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H. T. Tagian,
W. M. Abd-Elhameed,
G. M. Moatimid,
Y. H. Youssri,
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Abstract |
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| The current article is devoted to constructing modified shifted Gegenbauer polynomials and employing them to treat the second-order BVPs. The operational matrices of these polynomials are established. These operational matrices generalize some introduced operational matrices in the literature. Furthermore, they are employed along with suitable spectral methods to handle the linear and non-linear second-order BVPs. More precisely, the two spectral methods, namely, Petrov-Galerkin and collocation methods are applied to treat respectively the linear and non-linear BVPs. The feasibility of the presented algorithms is checked through some examples with individual kinds namely: singular, singularly perturbed, and Bratu-type equations.
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