Abstract
Parameter-robust numerical methods for a particular class of singularly perturbed quasilinear boundary value problems were constructed and analysed in Farrell et al. (Math Comp 78:103-127, 2009). Certain constraints were imposed in Farrell et al. (Math Comp 78:103-127, 2009) on the data to establish the final theoretical error bound. In this companion paper to Farrell et al. (Math Comp 78:103-127, 2009), the parameter-uniform performance of the numerical method is examined (via numerical experiments) when one or more of these constraints are violated. The numerical results in this paper suggest that the numerical approximations converge for a wider class of problems to that covered by the theoretical convergence analysis in Farrell et al. (Math Comp 78:103-127, 2009).
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References
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, and G.I. Shishkin, Robust Computational Techniques for Boundary Layers, Chapman and Hall/CRC, New York/Boca Raton, (2000)
P.A. Farrell, E. O'Riordan, and G.I. Shishkin, A class of singularly perturbed quasilinear differential equations with interior layers, Mathematics of Computation 78(265):103–127 (2009)
F.A. Howes, Boundary-interior layer interactions in nonlinear singular perturbation theory, Memoirs of the AMS 15:203 (1978)
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© 2009 Springer-Verlag Berlin Heidelberg
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Farrell, P.A., O’Riordan, E. (2009). Examination of the Performance of Robust Numerical Methods for Singularly Perturbed Quasilinear Problems with Interior Layers. In: Hegarty, A., Kopteva, N., O'Riordan, E., Stynes, M. (eds) BAIL 2008 - Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00605-0_10
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DOI: https://doi.org/10.1007/978-3-642-00605-0_10
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