A PETROV-GALERKIN METHOD FOR A SINGULARLY PERTURBED ORDINARY DIFFERENTIAL EQUATION WITH NON-SMOOTH DATA

  • Zheng T. (Department of Civil and Buikding Engineering, Loughborough University) ;
  • Liu F. (School of Mathematical Science, Queensland University of Technology)
  • 발행 : 2006.09.01

초록

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

키워드