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

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Knowledge-Based Intelligent Information and Engineering Systems (KES 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4693))

Abstract

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.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, P.R. China

    Zhongdi Cen

  2. School of Sciences, Jimei University, Xiamen 361021, China

    Xin Cai

Authors
  1. Zhongdi Cen
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  2. Xin Cai
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Editor information

Editors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, Via Comelico 39/41, 20135, Milano, Italy

    Bruno Apolloni

  2. Centre for SMART Systems, School of Engineering, University of Brighton, BN2 4GJ, Brighton, UK

    Robert J. Howlett

  3. Knowledge-Based Intelligent Engineering Systems Centre, University of South Australia, Mawson Lakes, SA 5095, Adelaide, Australia

    Lakhmi Jain

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© 2007 Springer-Verlag Berlin Heidelberg

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Cen, Z., Cai, X. (2007). A Second-Order Upwind Difference Scheme for a Singularly Perturbed Problem with Integral Boundary Condition in Netural Network. In: Apolloni, B., Howlett, R.J., Jain, L. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2007. Lecture Notes in Computer Science(), vol 4693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74827-4_22

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  • DOI: https://doi.org/10.1007/978-3-540-74827-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74826-7

  • Online ISBN: 978-3-540-74827-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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