Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials (Q1964173)
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scientific article; zbMATH DE number 1398880
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials |
scientific article; zbMATH DE number 1398880 |
Statements
Closed-form expressions for certain induction integrals involving Jacobi and Chebyshev polynomials (English)
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20 July 2000
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In the numerical solution of Cauchy singular integral equations (applied in airfoil theory, elasticity, and hydrodynamics) by collocation methods, certain non-singular mutual-induction integrals involving Jacobi and Chebyshev polynomials appear. However, the corresponding recursion scheme is seriously corrupted by numerical noise. The author shows that it is possible to derive closed-form expressions for these integrals that are free of such problems.
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Cauchy singular integral equations
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collocation methods
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boundary integral equations
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finite strip boundaries
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two-strip problem
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non-singular mutual-induction integrals
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recursion formulas
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orthogonal polynomials
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numerical instabilities
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trailing-edge singularity
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airfoil theory
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Jacobi and Chebyshev polynomials
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