Shivaranjani, N.; Miller, J. J. H.; Valarmathi, S. A parameter uniform almost first order convergent numerical method for a semi-linear system of singularity perturbed delay differential equations. (English) Zbl 1333.65086 Biomath 3, No. 2, 1411041, 8 p. (2014). MSC: 65L11 34K26 34K28 65L12 34A34 65L50 65L20 PDFBibTeX XMLCite \textit{N. Shivaranjani} et al., Biomath 3, No. 2, 1411041, 8 p. (2014; Zbl 1333.65086) Full Text: DOI
Shivaranjani, Nagarajan; Narasimhan, Ramanujam; Miller, J. J. H.; Valarmathi, Sigamani A parameter uniform method for an initial value problem for a system of singularly perturbed delay differential equations. (English) Zbl 1319.65060 Ansari, Ali R. (ed.), Advances in applied mathematics. Selected papers based on the presentations at the 1st Gulf international conference on applied mathematics 2013, GICAM ’13, Kuwait City, Kuwait, in cooperation with the Society for Industrial and Applied Mathematics, SIAM, November 19–21, 2013. Cham: Springer (ISBN 978-3-319-06922-7/hbk; 978-3-319-06923-4/ebook). Springer Proceedings in Mathematics & Statistics 87, 127-138 (2014). MSC: 65L05 65L03 34K28 65L11 65L12 65L50 34K06 65L20 PDFBibTeX XMLCite \textit{N. Shivaranjani} et al., Springer Proc. Math. Stat. 87, 127--138 (2014; Zbl 1319.65060) Full Text: DOI
Manikandan, M.; Shivaranjani, N.; Miller, J. J. H.; Valarmathi, S. A parameter-uniform numerical method for a boundary value problem for a singularly perturbed delay differential equation. (English) Zbl 1319.65064 Ansari, Ali R. (ed.), Advances in applied mathematics. Selected papers based on the presentations at the 1st Gulf international conference on applied mathematics 2013, GICAM ’13, Kuwait City, Kuwait, in cooperation with the Society for Industrial and Applied Mathematics, SIAM, November 19–21, 2013. Cham: Springer (ISBN 978-3-319-06922-7/hbk; 978-3-319-06923-4/ebook). Springer Proceedings in Mathematics & Statistics 87, 71-88 (2014). MSC: 65L10 65L11 65L03 34K06 34K26 65L12 65L20 65L50 34K28 PDFBibTeX XMLCite \textit{M. Manikandan} et al., Springer Proc. Math. Stat. 87, 71--88 (2014; Zbl 1319.65064) Full Text: DOI
Franklin, V.; Paramasivam, M.; Miller, J. J. H.; Valarmathi, S. Second-order parameter-uniform convergence for a finite difference method for a singularly perturbed linear parabolic system. (English) Zbl 1279.65104 Int. J. Numer. Anal. Model. 10, No. 1, 178-202 (2013). Reviewer: Martina Wirz (Braunschweig) MSC: 65M12 65M06 35B25 35K51 65M50 PDFBibTeX XMLCite \textit{V. Franklin} et al., Int. J. Numer. Anal. Model. 10, No. 1, 178--202 (2013; Zbl 1279.65104) Full Text: arXiv Link
Valarmathi, S.; Miller, John J. H. A parameter-uniform finite difference method for singularly perturbed linear dynamical systems. (English) Zbl 1198.65123 Int. J. Numer. Anal. Model. 7, No. 3, 535-548 (2010). Reviewer: Fernando Casas (Castellon) MSC: 65L12 65L05 65L20 65L70 34A30 34E15 PDFBibTeX XMLCite \textit{S. Valarmathi} and \textit{J. J. H. Miller}, Int. J. Numer. Anal. Model. 7, No. 3, 535--548 (2010; Zbl 1198.65123) Full Text: arXiv Link
Meenakshi, P. Maragatha; Valarmathi, S.; Miller, J. J. H. Solving a partially singularly perturbed initial value problem on Shishkin meshes. (English) Zbl 1208.65099 Appl. Math. Comput. 215, No. 9, 3170-3180 (2010). Reviewer: Thomas Sonar (Braunschweig) MSC: 65L05 34A34 34E15 65L20 65L12 65L50 PDFBibTeX XMLCite \textit{P. M. Meenakshi} et al., Appl. Math. Comput. 215, No. 9, 3170--3180 (2010; Zbl 1208.65099) Full Text: DOI
Valarmathi, S.; Miller, J. J. H. A parameter-uniform finite difference method for a singularly perturbed initial value problem: A special case. (English) Zbl 1179.65097 Hegarty, Alan F. (ed.) et al., BAIL 2008 – Boundary and interior layers. Proceedings of the international conference on boundary and interior layers – computational and asymptotic methods, Limerick, Ireland, July 28–August 1, 2008. Berlin: Springer (ISBN 978-3-642-00604-3/pbk; 978-3-642-00605-0/ebook). Lecture Notes in Computational Science and Engineering 69, 267-276 (2009). MSC: 65L12 65L10 65L05 34A30 65L20 65L50 34E15 PDFBibTeX XMLCite \textit{S. Valarmathi} and \textit{J. J. H. Miller}, Lect. Notes Comput. Sci. Eng. 69, 267--276 (2009; Zbl 1179.65097) Full Text: DOI
Farrell, P. A.; Hegarty, A. F.; Miller, J. J. H.; O’Riordan, E.; Shishkin, G. I. Robust computational techniques for boundary layers. (English) Zbl 0964.65083 Applied Mathematics and Mathematical Computation. 16. Boca Raton, FL: Chapman & Hall/ CRC Press. xvi, 254 p. (2000). Reviewer: Etienne Emmrich (Berlin) MSC: 65M06 35K57 65L12 65L10 65L20 65L70 35K15 34B05 34E15 65M15 35B25 65M12 76D10 76M20 65-02 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., Robust computational techniques for boundary layers. Boca Raton, FL: Chapman \& Hall/ CRC Press (2000; Zbl 0964.65083)
Farrell, Paul A.; Miller, John J. H.; O’Riordan, Eugene; Shishkin, Grigorii I. On the non-existence of \(\varepsilon\)-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems. (English) Zbl 0892.65055 Math. Comput. 67, No. 222, 603-617 (1998). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 65L12 34E15 34B15 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., Math. Comput. 67, No. 222, 603--617 (1998; Zbl 0892.65055) Full Text: DOI
Liu, Fawang; Fitzsimons, Conor J.; Miller, John J. H. Convergence of the nonconforming Wilson’s brick for arbitrary hexahedral meshes. (English) Zbl 0908.65098 Numer. Math., J. Chin. Univ. 6, No. 2, 184-199 (1997). Reviewer: Myron Sussman (Bethel Park) MSC: 65N30 65N15 74S05 65N12 35J25 PDFBibTeX XMLCite \textit{F. Liu} et al., Numer. Math., J. Chin. Univ. 6, No. 2, 184--199 (1997; Zbl 0908.65098)
Clavero, Carmelo; Lisbona, Francisco; Miller, John J. H. Uniform convergence of arbitrary order on nonuniform meshes for a singularly perturbed boundary value problem. (English) Zbl 0856.65089 J. Comput. Appl. Math. 59, No. 2, 155-171 (1995). MSC: 65L10 34B05 34E15 65L12 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Appl. Math. 59, No. 2, 155--171 (1995; Zbl 0856.65089) Full Text: DOI
Miller, J. J. H.; Wang, S. A new non-conforming Petrov-Galerkin finite-element method with triangular elements for a singularly perturbed advection-diffusion problem. (English) Zbl 0806.65111 IMA J. Numer. Anal. 14, No. 2, 257-276 (1994). Reviewer: S.C.Rajvanshi (Chandigarh) MSC: 65N30 65N12 65N50 65N15 35B25 35J25 PDFBibTeX XMLCite \textit{J. J. H. Miller} and \textit{S. Wang}, IMA J. Numer. Anal. 14, No. 2, 257--276 (1994; Zbl 0806.65111) Full Text: DOI
Miller, John J. H.; Wang, Song An \(\epsilon\)-uniformly convergent finite box method for a singularly perturbed advection-diffusion equation. (English) Zbl 0834.65106 Agarwal, R. P. (ed.), Contributions in numerical mathematics. Singapore: World Scientific Publishing Co. World Sci. Ser. Appl. Anal. Vol. 2, 271-284 (1993). MSC: 65N30 65N15 65N12 35J25 35B25 PDFBibTeX XMLCite \textit{J. J. H. Miller} and \textit{S. Wang}, in: Contributions in numerical mathematics. Singapore: World Scientific Publishing Co.. 271--284 (1993; Zbl 0834.65106)
Miller, J. J. H.; Shishkin, G. I. On the construction of uniformly convergent finite difference schemes for singularly perturbed problems for a quasilinear elliptic equation. (English) Zbl 0769.65073 Computational methods for boundary and interior layers in several dimensions, Adv. Comput. Methods Bound. Inter. Layers 1, 103-118 (1991). Reviewer: O.Titow (Berlin) MSC: 65N06 65N15 65N12 35J25 35B25 PDFBibTeX XMLCite \textit{J. J. H. Miller} and \textit{G. I. Shishkin}, Adv. Comput. Methods Bound. Inter. Layers 1, 103--118 (1991; Zbl 0769.65073)
Fitzsimons, C. J.; Miller, J. J. H.; Wang, S.; Wu, C. H. Hexahedral finite elements for the stationary semiconductor device equations. (English) Zbl 0725.65119 Comput. Methods Appl. Mech. Eng. 84, No. 1, 43-57 (1990). Reviewer: J.A.Crow (Corvallis) MSC: 65Z05 65N30 65N12 35Q60 78A55 35J65 PDFBibTeX XMLCite \textit{C. J. Fitzsimons} et al., Comput. Methods Appl. Mech. Eng. 84, No. 1, 43--57 (1990; Zbl 0725.65119) Full Text: DOI
Fitzsimons, C.; Miller, J. J. H.; O’Riordan, E. Fitted Petrov-Galerkin methods for singularly perturbed boundary value problems. (English) Zbl 0672.65066 BAIL III, Proc. 3rd Int. Conf. Boundary and interior layers, Dublin/Ireland 1984, Conf. Ser. 6, 209-214 (1984). MSC: 65L10 65L60 34B05 34E15 PDFBibTeX XML
Miller, J. J. H. Some finite difference schemes for a singular perturbation problem. (English) Zbl 0446.65042 Constructive function theory, Proc. int. Conf., Blagoevgrad 1977, 399-402 (1980). MSC: 65L10 34D15 34B05 PDFBibTeX XML
Carroll, John; Miller, J. J. H. Completely exponentially fitted finite difference schemes for some singular perturbation problems. (English) Zbl 0441.65063 Boundary and interior layers - computational and asymptotic methods, Proc. Conf., Dublin 1980, 225-230 (1980). MSC: 65L10 34D15 34B05 65L07 PDFBibTeX XML
Miller, John J. H. On the convergence, uniformly in \(\varepsilon\), of difference schemes for a two point boundary singular perturbation problem. (English) Zbl 0419.65051 Numerical analysis of singular perturbation problems, Proc. Conf. Nijmegen 1978, 467-474 (1979). MSC: 65L10 34B05 34E15 PDFBibTeX XML
Miller, John J. H. Some finite difference schemes for a singular perturbation problem. (English) Zbl 0396.65047 Constructive function theory, Proc. int. Conf., Blagoevgrad 1977 (to appear). MSC: 65L10 34D15 34B05 PDFBibTeX XML