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Numerical Treatment of Special Types of Odd-Order Boundary Value Problems Using Nonsymmetric Cases of Jacobi Polynomials |
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PP: 305-319 |
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doi:10.18576/pfda/080210
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Author(s) |
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Waleed Mohamed Abd-Elhameed,
Eid Hassan Doha,
Muhammad Mahmoud Alsuyuti,
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Abstract |
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| In this article, two new dual Petrov-Galerkin algorithms for solving high odd-order boundary value problems (BVPs) are presented and implemented. The philosophy of applying the Petrov-Galerkin method is built on choosing the trial and test functions such that they satisfy the underlying boundary and dual boundary conditions, respectively. The presented approaches are based on employing the shifted Chebyshev polynomials of third and fourth kinds, respectively, as basis functions. Several numerical experiments are included to ascertain the validity and efficiency of the proposed algorithms. Moreover, comparisons with some other numerical methods in the literature are given.
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