Research Interests

Numerical analysis of singularly perturbed differential equations. Layer resolving meshes. Computational Fluid Dynamics

 

   

Edited Books

Sharon Flynn, Ted Hurley, Micheal Mac an Airchinnigh, Niall Madden, Michael McGettrick, Michel Schellekens and Anthony Seda (Ed.). (2003) The Second Irish Conference on the Mathematical Foundations of Computer Science and Information Technology (MFCSIT 2002). x: Electronic Notes in Theoretical Computer Science (Elsevier). [DOI] [Details]

Peer Reviewed Journals

Madden, N., Stynes, M. (1996) 'Linear enhancements of the streamline diffusion method for convection-diffusion problems'. COMPUTERS AND MATHEMATICS WITH APPLICATIONS, 32 :29-42. [Details]

Madden N., Stynes M. (1997) 'Efficient generation of oriented meshes for solving convection-diffusion problems'. INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENG, 40 :565-576. [Details]

Linss, T., Madden, N. (2003) 'An improved estimate for a numerical method for a system of coupled singularly perturbed reaction-diffusion equations'. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 3 (3):417-423. [Details]

Madden, N,Stynes, M (2003) 'A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems'. Ima Journal Of Numerical Analysis, 23 :627-644. [Details]

Linss, T,Madden, N (2004) 'Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations'. Computing, 73 :121-133. [DOI] [Details]

Linss, T,Madden, N (2004) 'A finite element analysis of a coupled system of singularly perturbed reaction-diffusion equations'. Applied Mathematics And Computation, 148 :869-880. [DOI] [Details]

Kopteva, N,Madden, N,Stynes, M (2005) 'Grid equidistribution for reaction-diffusion problems in one dimension'. Numerical Algorithms, 40 :305-322. [DOI] [Details]

Linss, T,Madden, N (2007) 'Parameter uniform approximations for time-dependent reaction-diffusion problems'. Numerical Methods For Partial Differential Equations, 23 :1290-1300. [DOI] [Details]

Newell, J,Higgins, D,Madden, N,Cruickshank, J,Einbeck, J,McMillan, K,McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, 25 :1403-1409. [DOI] [Details]

Kellogg, RB,Madden, N,Stynes, M (2008) 'A parameter-robust numerical method for a system of reaction-diffusion equations in two dimensions'. Numerical Methods For Partial Differential Equations, 24 :312-334. [DOI] [Details]

Liu, F., Madden, N., Stynes, M., Zhou, A. (2009) 'A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions'. IMA JOURNAL OF NUMERICAL ANALYSIS, 29 (4):986-1007. [DOI] [Details]

Linss, T., Madden, N. (2009) 'Layer-adapted meshes for a system of coupled singularly perturbed reaction-diffusion problems'. IMA JOURNAL OF NUMERICAL ANALYSIS, 29 (1):109-125. [DOI] [Details]

Stephens, M., Madden, N. (2009) 'A Parameter-Uniform Schwarz Method for a Coupled System of Reaction Diffusion Equations'. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 230 (2):360-370. [DOI] [Details]

Stephens, M., Madden, N. (2009) 'A Schwarz technique for a system of reaction diffusion equations with differing parameters'. LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING, 69 :247-255. [Details]

Linss, T., Madden, N. (2010) 'Analysis of an alternating direction method applied to singularly perturbed reaction-diffusion problems'. International Journal of Numerical Analysis and Modelling, 7 (3):507-519. [Details]

Niall Madden and Kajal Kumar Mondal (2011) 'Improved mathematical and numerical modelling of dispersion of a solute from a continuous source'. Lecture Notes In Computational Science And Engineering, 81 :177-185. [Details]

Naresh M. Chadha and Niall Madden (2011) 'A two-weight scheme for a time-dependent advection-diffusion problem'. Lecture Notes In Computational Science And Engineering, 85 :99-108. [DOI] [ARAN Link] [Details]

 

Conference Publications

Catherine G. Enright & Michael G. Madden (NUI Galway), Stuart J. Russell & Norm Aleks (UC Berkeley), Geoffrey Manley (UCSF), John Laffey (NUI Galway), Brian Harte & Anne Mulvey (University Hospital Galway), Niall Madden (NUI Galway) (2010) Modelling Glycaemia in ICU Patients: A Dynamic Bayesian Network Approach Proceedings of BIOSIGNALS-2010, Part of the 3rd International Joint Conference on Biomedical Engineering Systems and Technologies Valencia, Spain, [Details]

Catherine G. Enright and Michael G. Madden and Niall Madden and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs . In: Mor Peleg and Nada Lavrac and Carlo Combi eds. AIME , pp.159-168 [Details]

Catherine G. Enright, Michael G. Madden, Niall Madden, and John G. Laffey (2011) Clinical Time Series Data Analysis Using Mathematical Models and DBNs Proc. 13th Conference on Artificial Intelligence in Medicine Slovenia, [Details]

                   

Conference Paper

Kopteva, N., Madden, N., Stynes, M. (2004) On equidistribution for reaction-diffusion problems. Workshop on problems with boundary-layer phenomena. University of Limerick: Conference Paper [Details]

Niall Madden, Martin Stynes, and Gareth Thomas (2004) On the application of robust numerical methods to a complete flow wave-current model. Boundary and Interior Layers ONERA. Conference Paper [ARAN Link] [Details]

Madden, N., Bruce, R., Kellogg, B., Stynes, M. (2006) A parameter-robust numerical method for a coupled system of two dimensional reaction-diffusion equations. 4th Conference on Finite Difference Methods: Theory and Applications. Lozenetz, Bulgaria: Conference Paper [Details]

                                                                                                   

Working Paper

Madden, N., Stynes, M. (2007) On the numerical solution of a system of M singularly perturbed reaction-diffusion equations in two dimension. 6th Annual Workshop on Numerical Methods for Problems with Layer Phenomena. University of Limerick: Working Paper [Details]

   

Current Postgraduate Students

Anh Nhan, Masters - Research - Master of Science   -   Supervisor