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Personal profile

Research interests

My main research interest is the numerical approximation of time dependent partial differential equations (PDEs) and associated integral equations. This includes work on Volterra integral equations, methods for time domain boundary integral formulations of wave propagation problems and new methods for wave equation PDEs.

Roles & Responsibilities

Current Role

  • Deputy Director, Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), an EPSRC/SFC Centre for Doctoral Training

Teaching:

  • Numerical analysis of ODEs, 4th year,MMath,MSc course F10NC/F11NC
  • Mathematics for Engineers and Scientists 2, F17XB2
  • SMSTC Applied Mathematics Methods, 2 weeks on numerical ODEs.

Recent PhD Students:

  • Ali Alshomrani (jointly with Jack Carr, Heriot-Watt)
    Analysis and approximation of a nonlocal equation, 2014.
  • Matab Al-Ghamdi (Jack Carr was the main supervisor)
    Topics in coagulation-fragmentation equations, 2014,
  • Morag Macpherson (jointly with Andy White, Heriot-Watt, and Ross Davidson, SAC)
    Modelling population and disease dynamics in complex ecological systems, 2014

Recent Roles:

  • Director of Scottish Mathematical Sciences Training Centre (for PhD students)
  • Scientific Director, Numerical Algorithms and Intelligent Software (NAIS) Centre
  • Chair of Heriot-Watt Quality and Standards Committee
  • Member of Management Group, Centre for Analysis and Nonlinear PDEs
  • Treasurer of the committee of the UK Heads of Department of Mathematical Sciences
  • Member of Senate
  • Member of Senate Business Committee

 

Biography

I am from Tayport in North East Fife and I attended Bell-Baxter High School in Cupar. Other details are below.

1975-79St Andrews University, BSc in Applied Mathematics.
1979-82Dundee Univeristy, PhD in numerical analysis
1982-86Atomic Energy of Canada Ltd., mathematician and numerical analyst
1986-Heriot-Watt University, Department of Mathematics

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Research Output

Convolution-in-time approximations of time domain boundary integral equations

Davies, P. J. & Duncan, D. B., 2013, In : SIAM Journal on Scientific Computing. 35, 1, p. B43-B61 19 p., 088190.

Research output: Contribution to journalArticle

Open Access
File
  • 13 Citations (Scopus)
    55 Downloads (Pure)

    Finite-dimensional coagulation-fragmentation dynamics

    Carr, J., Al Ghamdi, M. & Duncan, D. B., 21 Mar 2018, In : Mathematical Models and Methods in Applied Sciences. 28, 05, p. 851-868 18 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 28 Downloads (Pure)

    Numerical approximation of first kind Volterra convolution integral equations with discontinuous kernels

    Davies, P. J. & Duncan, D. B., 27 Mar 2017, In : Journal of Integral Equations and Applications. 29, 1, p. 41-73 33 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 1 Citation (Scopus)
    104 Downloads (Pure)

    Incorporating habitat distribution in wildlife disease models: conservation implications for the threat of squirrelpox on the Isle of Arran

    Macpherson, M., Davidson, R. S., Duncan, D. B., Lurz, P. W., Jarrott, A. & White, A., Feb 2016, In : Animal Conservation. 19, 1, p. 3-14 12 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 8 Citations (Scopus)
    50 Downloads (Pure)

    Convolution spline approximations of Volterra integral equations

    Davies, P. J. & Duncan, D. B., 31 Oct 2014, In : Journal of Integral Equations and Applications. 26, 3, p. 369-410 42 p.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 8 Citations (Scopus)
    77 Downloads (Pure)