Reliable Computing

, Volume 2, Issue 2, pp 173–179 | Cite as

Numerical solutions of Burgers’ equation with a large Reynolds number

  • Masaaki Sugihara
  • Seiji Fujino


In this article the exact solution of Burgers’ equation represented as an infinite series is transformed into a simpler form involving the elliptic functionϑ3(υ, q). To evaluateϑ3(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.


Mathematical Modeling Reynolds Number Exact Solution Computational Mathematic Simple Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Численные рещения уравнения Бюргера при боьшом числе Рейнольдса


Прелтожено преобраэование тонного решения уравнения Бюргера, представленного в виде бесконечного ряда, в более простую Форму с иснольэованием эллинтической Функдииϑ3(υ, q). Дяя вычисленияϑ3(υ, q) испольэуется мнимое преобраэование Якоби. Покаэано, что иолученные таким обраэом решения являются численно устойчивыми и точными.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Caldwell, J. and Smith, P.Solution of Burgers’ equation with a large Reynolds number. Appl. Math. Modelling6 (1982), pp. 381–385.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Cole, J. D.On a quasi-linear parabolic equation occurring in aerodynamics. Quart. Appl. Math.9 (1951), pp. 225–236.MATHMathSciNetGoogle Scholar
  3. [3]
    Hopf, E.The partial differential equation u t +uu x=μu xx. Commun. Pure Appl. Math.3 (1950), pp. 201–230.MATHMathSciNetGoogle Scholar
  4. [4]
    Kakuda, K. and Tosaka, N.The generalized boundary element approach to Burgers’ equation. Int. J. Num. Meths. Engrg.29 (1990), pp. 245–261.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Masaaki Sugihara
    • 1
  • Seiji Fujino
    • 2
  1. 1.Faculty of EngineeringUniversity of TokyoTokyoJapan
  2. 2.Faculty of Information SciencesHiroshima City UniversityHiroshimaJapan

Personalised recommendations