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Numerical solutions of Burgers’ equation with a large Reynolds number

Численные рещения уравнения Бюргера при боьшом числе Рейнольдса

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Reliable Computing

Abstract

In this article the exact solution of Burgers’ equation represented as an infinite series is transformed into a simpler form involving the elliptic functionϑ 3(υ, q). To evaluateϑ 3(υ, q), we use the Jacobi Imaginary Transformation. It is made clear that the solutions obtained by the proposed approach are numerically stable and precise.

Abstract

Прелтожено преобраэование тонного решения уравнения Бюргера, представленного в виде бесконечного ряда, в более простую Форму с иснольэованием эллинтической Функдииϑ 3(υ, q). Дяя вычисленияϑ 3(υ, q) испольэуется мнимое преобраэование Якоби. Покаэано, что иолученные таким обраэом решения являются численно устойчивыми и точными.

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Authors and Affiliations

  1. Faculty of Engineering, University of Tokyo, 7-3-1, Hongou, Bunkyo-ku, 113, Tokyo, Japan

    Masaaki Sugihara

  2. Faculty of Information Sciences, Hiroshima City University, 151-5, Ozuka, Numata-cho, Asaminami-ku, 731-31, Hiroshima, Japan

    Seiji Fujino

Authors
  1. Masaaki Sugihara
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  2. Seiji Fujino
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© M. Sugihara, S. Fujino, 1996

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Sugihara, M., Fujino, S. Numerical solutions of Burgers’ equation with a large Reynolds number. Reliable Comput 2, 173–179 (1996). https://doi.org/10.1007/BF02425921

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  • DOI: https://doi.org/10.1007/BF02425921

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