Marcus Garvie

Associate Professor, Mathematics
Phone number: 
519-824-4120 x53409
MacNaughton 552

My doctoral training was in the rigorous numerical analysis and mathematical analysis of parabolic partial differential equations using the finite element method. Most of my experience has been in the area of the numerics of reaction-diffusion equations using the standard Galerkin finite element method. The main application area is mathematical biology, with a focus on spatially extended predator-prey interactions in ecology. I have also worked in optimal control theory and studied diffusion-induced instability (Turing theory). For further details, please visit my website. 

In addition to my research skills I have extensive teaching experience gained from secondary school level positions, teaching at the community college level, and also from the post of Mathematics Instructor at Arizona State University in the USA. I fully funded my PhD studies through teaching and in the UK I am a qualified teacher at the secondary school level. I enjoy teaching at all levels and at Guelph I currently teach large classes at the first year level in Business Mathematics and Linear Algebra. I also teach a large class (of mainly Engineers) at the 2nd year level in Numerical Methods. I have put a lot of effort into creating well-written workbooks for all my courses, so that my classes are now textbook-independent. I am also excited about the prospect of making my classes relevant to the real world, for example, by including applications and computer examples. 

  • Mathematical and numerical analysis
  • Mathematical biology/ecology
  • Optimal control theory
  • Turing theory

B.Sc. in Mathematics (University of Sussex), 1989.

M.Sc. in Ecology (The University of Wales, Bangor), 1991.

Postgraduate Certificate in Education (Keele University), 1993.

M.Sc. in The Numerical Solution of Differential Equations (University of Reading), 1998.

Ph.D. in Applied Mathematics (University of Durham), 2003.

Preprints of all papers are available at The Atrium, University of Guelph Institutional Repository

Published Papers

  1. Diele F. and Garvie M.R. and Trenchea C. (2017), " Numerical analysis of a first-order in time implicit-symplectic scheme for predator-prey systems " Computers and Mathematics with Applications, Vol. 74. No. 5, pp. 948-961.
  2. Garvie M.R. and Morgan J. and Sharma V. (2017), "Finite element approximation of a spatially structured metapopulation PDE model " Computers and Mathematics with Applications, Vol. 74. No. 5, pp. 934–947.
  3. Garvie M.R., Burkardt J. and Morgan J. (2015), "Simple Finite Element Methods for Approximating Predator-Prey Dynamics in Two Dimensions Using MATLAB " Bulletin of Mathematical Biology, Vol. 77. No. 3, pp. 548-578.
  4. Garvie M.R. and Trenchea C. (2011), "Identification of space-time distributed parameters in the Gierer-Meinhardt reaction-diffusion system " SIAM Journal on Applied Mathematics, Vol. 74, No. 1, pp. 147-166.
  5. Garvie M.R. and Trenchea C. (2011), "A three level finite element approximation of a pattern formation model in developmental biology," published in Numerische Mathematik (online first DOI 10.1007/s00211-013-0591-z).
  6. Garvie M.R., Maini P.K. and Trenchea C. (2010), "An efficient and robust numerical algorithm for estimating parameters in Turing systems," published in Journal of Computational Physics, Vol. 229, pp. 7058-7071.
  7. Schwalb A.N., Garvie M.R. and Ackerman J.D. (2010), "Dispersion of freshwater mussel larvae in a lowland river," published in Limnology and Oceanography, Vol. 55 No. 2, pp. 628-638.
  8. Garvie M.R. and Trenchea C. (2010), "Spatiotemporal dynamics of two generic predator-prey models," published in Journal of Biological Dynamics, Vol. 4 No. 6, pp. 559-570.
  9. Garvie M.R. and Golinski M. (2010) , "Metapopulation dynamics for spatially-extended predator-prey interactions," published in Ecological Complexity, Vol. 7 No. 2, pp. 55-59.
  10. Garvie M.R. and Trenchea C. (2007) , "Optimal control of a 'nutrient-phytoplankton-zooplankton-fish' system," published in SIAM Journal On Control and Optimization, Vol. 46 No. 3, pp. 775-791.
  11. Garvie M.R. (2007) , "Finite difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB," published in Bulletin of Mathematical Biology, Vol. 69. No. 3, pp. 931-956.
  12. Garvie M.R. and Trenchea C. (2007), "Finite element approximations of spatially extended predator-prey interactions with the Holling type II functional response," published in Numerische Mathematik, Vol. 107, pp. 641-667.
  13. Garvie M.R. and Blowey J.F. (2005), "A reaction-diffusion system of lambda-omega type. Part II: numerical analysis," published in European Journal of Applied Mathematics, Vol. 16 No. 05 , pp. 621-646.
  14. Blowey J.F. and Garvie M.R. (2005), "A reaction-diffusion system of lambda-omega type. Part I: mathematical analysis," published in European Journal of Applied Mathematics, Vol. 16 No. 01 , pp. 1-19.

Conference Proceedings

  1. Trenchea C. and Garvie M.R. , "Biomanipulation of Food-Webs in Eutrophic Lakes.," published in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, USA.