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Bernstein-polynomials based Filon method for highly oscillatory integrals
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DOI：10.1016/j.cam.2025.117191.png)
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摘要
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A modified formulation based on Bernstein polynomials is proposed for the numerical solution of highly oscillatory integrals within a Filon-type framework, aiming to suppress spurious oscillations arising from the Runge phenomenon. When the amplitude function of a highly oscillatory integral exhibits the Runge phenomenon, a Bernstein polynomial-based collocation method with Chebyshev-Gauss-Lobatto nodes is employed within the Filon framework to compute the oscillatory integral. To evaluate the desired moments, various techniques are implemented in the current work. The oscillatory integrals with stationary points are approximated using a domain-splitting algorithm and moment-free modified Filon-type method. A theoretical analysis is provided establishing error bounds in terms of the inverse power of the frequency parameter omega. The predicted order of convergence is verified numerically through a series of benchmark test cases.
Keyword:
Bernstein interpolants with Chebyshev-Gauss-Lobatto nodes
Filon-type method
Runge or Gibbs phenomenon
Stationary point
期刊
J
IF:
2.6
论文数:
338
被引数:
0
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