Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods

INAN B., BAHADIR A. R.

PRAMANA-JOURNAL OF PHYSICS, cilt.81, sa.4, ss.547-556, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 81 Sayı: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s12043-013-0599-z
  • Dergi Adı: PRAMANA-JOURNAL OF PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.547-556
  • İnönü Üniversitesi Adresli: Evet

Özet

This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equation. As the Burgers' equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton's method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.