A Second-Order Upwind Difference Scheme for a Singularly Perturbed Problem with Integral Boundary Condition in Netural Network
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.
KeywordsSingular perturbation upwind difference scheme Shishkin mesh uniform convergence
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- 2.de Boor, C.: Good approximation by splines with variable knots. In: Meir, A., Sharma, A. (eds.) Spline Functions and Approximation Theory. In: Proceedings of Symposium held at the Unoversity of Alberta, Edmonton, May 29-June 1, 1972, Birkhäuser, Basel (1973)Google Scholar
- 8.Samoilenko, A.M., Ronto, N.I., Martynyuk, S.V.: On the numerical-analytic method of problems with integral boundary conditions. Dokl. Akad. Nauk. Ukrain. SSR 4 (in Russian) 4, 34–37 (1991)Google Scholar