Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: In this article, an application of the Fourier series to the most significant digit problem is presented, where the authors show that it can be used to solve the problem of the largest digit problem.
Abstract: (1994). An Application of Fourier Series to the Most Significant Digit Problem. The American Mathematical Monthly: Vol. 101, No. 9, pp. 879-886.
74 citations
TL;DR: A spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition.
74 citations
TL;DR: In this article, two analytical solutions for the stepwise cyclic diffusion problem in a spherical particle have been presented, one based on a Fourier series expansion, and the other based on penetration theory.
74 citations
TL;DR: In this article, a numerical method for the calculation of wave properties is presented, which involves expanding the velocity components and the equation of the profile in Fourier series and determining the Fourier coefficients numerically by the method of least squares from the Bernoulli equation and from the equation insuring that the particle motion at the surface matches the profile motion.
Abstract: A numerical method for the calculation of wave properties is presented. It involves expanding the velocity components and the equation of the profile in Fourier series and determining the Fourier coefficients numerically by the method of least squares from the Bernoulli equation and from the equation insuring that the particle motion at the surface matches the profile motion. An iterative procedure is used, since the velocity coefficients depend upon the profile coefficients, and vice versa. The calculations seem always to converge to an answer, although slowly. To judge the accuracy obtained, a comparison has been made with the Stokes waves. In every case the direct method is less in error.
74 citations
TL;DR: This work clarifies the possible scope of steerability by Fourier decompositions, and approximate steerability with a limited number of basis functions, and the singularity that occurs when steering the scale.
74 citations