Kowloon Tong, Hong Kong

- 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.
- Discontinuous Galerkin methods for Volterra functional integral and differential equations

- (with Liang Hui) The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations, SIAM J. Numer. Anal., 57 (2019), pp. 1875-1896.
- (with Liang Hui) Collocation methods for integro-differential algebraic equations with index 1, IMA J. Numer. Anal., 39 (2019), 36pp.
- (with H.M. Song and Z.W. Yang) Analysis of collocation methods for nonlinear Volterra integral equations of the third kind, Calcolo, 56 (2019), 29pp.
- Numerical analysis and computational solution of integro- differential equations, in: Contemporary Computational Mathematics -- A Celebration of the 80th birthday of Ian Sloan (J. Dick et al., eds.), Vol. 1, 208-231, Springer, 2018.
- (with S. Seyed Allaei and Z.W. Yang) Collocation methods for third-kind Volterra integral equations, IMA J. Numer. Anal., 37 (2017), 1104-1124.
- H. Brunner (with S. Gourley, H.S. Liu and Y.Y. Xiao), Pauses of larval development and their consequences for stage-structured populations, SIAM J. Appl. Math., 77 (2017), 977-994.
- "Volterra Integral Equations: An Introduction to Theory andÂ Applications", Cambridge Monographs on Applied and Computational Mathematics, No. 30, Cambridge University Press, Cambridge/UK, January 2017. (See also: http://www.cambridge.org/9781107098725)
- (with H. Liang) Integral-algebraic equations: theory of collocation methods II, SIAM J. Numer. Anal., 54 (2016), 2640-2663.
- (with T. Tao and J.W. Zhang) Numerical blow-up of nonlinear parabolic integro-differential equations on unbounded domain, J. Sci. Comput., 68 (2016), 1281-1298.
- (with R. Zhang and H. Liang) Analysis of collocation methods for auto-convolution Volterra integral equations, SIAM J. Numer. Anal., 54 (2016), 899-920.
- (with Q.M. Huang and X.X. Xu) Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type, Discrete Contin. Dyn. Syst., 36 (2016), 5423-5443.
- (with Y.Y. Ma and Y.S. Xu) The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels, J. Integral Equations Appl., 27 (2015), 455-487.
- (with S. Seyed Allaei and Z.-W. Yang) Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations, J. Integral Equations Appl., 27 (2015), 325-342.
- (with H.D. Han and D.S. Yin) The maximum principle for time-fractional diffusion equations and its application, Numer. Funct. Anal., 36 (2015), 1307-1321.
- (with Z.W. Yang) Quenching analysis for nonlinear Volterra integral equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 21 (2014), 507-529.
- (with H.D. Han and D.S. Yin) Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain, J. Comput. Phys., 276 (2014), 541-562.
- On Volterra integral operators with highly oscillatory kernels, Discrete Contin. Dyn. Syst., 34 (2014), 915-929.
- (with H. Liang) Integral-algebraic equations: theory of collocation methods I, SIAM J. Numer. Anal., 51 (2013), 2238-2259.
- (with Z.W Yang) Blow-up behavior of collocation solutions to Hammerstein-type Volterra integral equations, SIAM J. Numer. Anal., 51 (2013), 2260-2282.
- (with H.H. Xie and R. Zhang) Collocation methods for general Volterra functional integral equations with vanishing delays, SIAM J. Sci. Comput., 33 (2011), 3303-3332.
- (with A. Iserles and S.P. Norsett) The computation of the spectra of highly oscillatory Fredholm integral operators, J. Integral Equations Appl., 23 (2011), 467-519.
- (with K. Mustapha, H. Mustapha and D. Schoetzau) An hp-version 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 Q.M. Huang and H.H. Xie) Discontinuous Galerkin methods for delay differential equations of pantograph type, SIAM J. Numer. Anal., 48 (2011), 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 H. Liang) Stability of collocation methods for delay diferential equations with vanishing delays, BIT Numer. Math., 50 (2010), 693-711.
- (with X.N. Wu and J.W. Zhang) Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains, SIAM J. Sci. Comput., 31 (2010), 4478-4496.
- (with S. Maset) Time transformations for state-dependent delay differential equations, Commun. Pure Appl. Anal., 9 (2010), 23-45.
- (with D. Schoetzau) hp-discontinuous Galerkin time-stepping for Volterra integro-differential equations, SIAM J. Numer. Anal., 44 (2006), 224-245.
- (with N.-N. Yan) Finite element methods for optimal control problems governed by integral equations and integro-differential equations, Numer. Math., 101 (2005), 1-27.
- 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)

- Editorial Boards:
- SIAM Journal on Numerical Analysis
- IMA Journal of Numerical Analysis
- Journal of Integral Equations and Applications

- NSERC (Natural Sciences and Engineering Research Council of Canada):
- Member, Committee on Grants and Scholarships (COGS)
- Group Chair, Pure/Applied Mathematics and Statistical Sciences (2006-2009)

- AARMS (Atlantic Association for Research in the Mathematical
Sciences)
- Chair, Board of Directors (October 2009 - April 2013)

- 2008 David Borwein Distinguished Career Award (Canadian Mathematical Society)
- Fellow of the Fields Institute