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

Authors:
Zhongdi Cen;Xin Cai
Affiliations:
Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, P.R. China;School of Sciences, Jimei University, Xiamen 361021, China
Venue:
KES '07 Knowledge-Based Intelligent Information and Engineering Systems and the XVII Italian Workshop on Neural Networks on Proceedings of the 11th International Conference
Year:
2007

Citing 2
Cited 0

Differential equations with integral boundary conditions

Journal of Computational and Applied Mathematics
Extensions of quasilinearization method for differential equations with integral boundary conditions

Mathematical and Computer Modelling: An International Journal

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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.