A Second-Order Upwind Difference Scheme for a Singularly Perturbed Problem with Integral Boundary Condition in Netural Network

  • Zhongdi Cen
  • Xin Cai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4693)


In this paper we consider a first order singularly perturbed quasilinear boundary value problem with integral boundary condition which arises in netural network. The problem is discretized using a hybrid upwind difference scheme on a Shishkin mesh. Applying the discrete maximum principle and barrier function techniques we show that the scheme is almost second order convergent, in the discrete maximum norm, independently of singular perturbation parameter. Numerical experiments support these theoretical results.


Singular perturbation upwind difference scheme Shishkin mesh uniform convergence 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Zhongdi Cen
    • 1
  • Xin Cai
    • 2
  1. 1.Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100P.R. China
  2. 2.School of Sciences, Jimei University, Xiamen 361021China

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