- Numerical analysis of Volterra-type integral and integro-differential equations, including equations with weakly singular kernels and delay arguments.
- Computational solution of nonlinear reaction-diffusion problems with memory terms and blow-up solutions.
- (with K. Mustapha, H. Mustapha and D. Schoetzau) An hp-discontinuous Galerkin method for integro-differential equations of parabolic type, SIAM J. Numer. Anal., 49 (2011), 1369-1396.
- (with H. Han and J. Zhang) Numerical blow-up of semilinear parabolic PDEs on unbounded domains, J. Sci. Comput., 49 (2011), 367-382.
- (with H. Xie and R. Zhang) Analysis of collocation solutions for a class of functional equations with vanishing delays, IMA J. Numer. Anal., 31 (2011), 698-718.
- (with Q, Huang and H. Xie) Discontinuous Galerkin methods for delay differential equations of pantograph type, SIAM J. Numer. Anal., 48 (2010), 1944-1967.
- (with A. Boettcher, A. Iserles and S.P. Norsett) On the singular values and eigenvalues of the Fox-Li and related operators, New York J. Math., 16 (2010), 539-561.
- (with S. Maset) Time transformations for state-dependent delay differential equations, Commun. Pure Appl. Anal., 9 (2010), 23-45.
- (with D. Schoetzau) hp-discontinuous time-stepping for Volterra integro-differential equations, SIAM J. Numer. Anal., 44 (2006), 224-245.
- (with Q.-Y. Hu) Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays, SIAM J. Numer. Anal., 43 (2005), 1935-1949.
- Survey article: “The numerical analysis of functional integral and integro-differential equations of Volterra type”, Acta Numerica (2004), 55-145.
- Research monograph: “Collocation Methods for Volterra Integral and Related Functional Differential Equations”, Cambridge Monographs on Applied and Computational Mathematics, No. 15, Cambridge University Press, Cambridge/UK, November 2004 (xiv + 597 pages). (See also: www.cambridge.org)
- Chair, Board of Directors, Atlantic Association for Research in the Mathematical Sciences (AARMS) (2009- ).
- Member of Editorial Boards:
- SIAM Journal on Numerical Analysis.
- IMA Journal of Numerical Analysis.
- Journal of Integral Equations and Applications
- Canadian Mathematical Society's 2008 David Borwein Distinguished Career Award
- Fellow of the Fields Institute (June 2006)
- Member of COGS (Committee on Grants and Scholarships) (2006-2009)
- Group Chair, Mathematics and Statistical Sciences (2006-2009)