A numerical solution of Burgers' equation based on least squares approximation


AKSAN E., OZDES A., Ozis T.

APPLIED MATHEMATICS AND COMPUTATION, cilt.176, ss.270-279, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 176 Konu: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.amc.2005.09.045
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Sayfa Sayıları: ss.270-279

Özet

Burgers' equation which is one-dimensional non-linear partial differential equation was converted to p non-linear ordinary differential equations by using the method of discretization in time. Each of them was solved by the least squares method. For various values of viscosity at different time steps, the numerical solutions obtained were compared with the exact solutions. It was seen that both of them were in excellent agreement. While the exact solution was not available for viscosity smaller than 0.01, it was shown that mathematical structure of the equation for the obtained numerical solutions did not decay. (c) 2005 Elsevier Inc. All rights reserved.