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 Runge's phenomenon

In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions. The discovery was important because it shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations.

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updated Sun. February 5, 2023

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10 at the MDC Runge Conservation Nature Center, 330 Commerce ... 14 at the MDC Northeast Regional Office, 3500 S. Baltimore in Kirksville.

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The observed phenomenon, apart from the fundamental interest, provides a ..... which provided the fastest convergence compared with the Runge–Kutta and ... Thus, all trajectories for the Stokes parameter s0 have the same ...


 

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