Abstract
In this paper, we propose a second–order parameter–uniform convergent hybrid scheme for self–adjoint singular perturbation problems (SPPs) subject to mixed (Robin) type conditions. The cubic spline baesd difference scheme is combined with the classical central difference scheme to obtain monotone scheme. Numerical example is provided to support the theory.
Subject Classification: AMS 65L10 CR G1.7.
Chapter PDF
Similar content being viewed by others
Keywords
References
Chin, R.C.Y., Krasny, R.: A hybrid asymptotic finite-element method for stiff twopoint boundary-value problems. SIAM J. Sci. and Stat. Comput. 4, 229–243 (1983)
Farrell, P.A., Hegarty, A.F., Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Robust Computational Techniques for Boundary Layers. Chapman & Hall/CRC Press (2000)
Gracia, J.L., Lisbona, F., Clavero, C.: High order ε-uniform methods for singularly perturbed reaction-diffusion problems. LNCS, vol. 1998, pp. 350–358. Springer, Heidelberg (2001)
Miller, J.J.H., O’Riordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore (1996)
Pearson, C.E.: On a differential equation of boundary layer type. J. Math. Phys. 47(144), 134–154 (1968)
Roos, H.-G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Springer, Berlin (1996)
Stojanovic, M.: Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation. Publications de L’institut Mathematique 43(57), 155–163 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bawa, R.K., Natesan, S. (2005). Uniformly Convergent Computational Technique for Singularly Perturbed Self-adjoint Mixed Boundary-Value Problems. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428862_183
Download citation
DOI: https://doi.org/10.1007/11428862_183
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26044-8
Online ISBN: 978-3-540-32118-7
eBook Packages: Computer ScienceComputer Science (R0)