If you made any changes in Pure these will be visible here soon.

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


  • 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



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

Fingerprint Dive into the research topics where Dugald Black Duncan is active. These topic labels come from the works of this person. Together they form a unique fingerprint.

Volterra Integral Equations Mathematics
Integral Equations Mathematics
Approximation Mathematics
Numerical Approximation Mathematics
Stability and Convergence Mathematics
Convolution Mathematics
Collocation Mathematics
Time Domain Mathematics

Co Author Network Recent external collaboration on country level. Dive into details by clicking on the dots.

Research Output 1989 2018

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
Galerkin Approximation
Boundary Integral
Volterra Integral Equations
Stability and Convergence
Scattering Problems

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
Center Manifold
Numerical Approximation

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
Convolution Equation
Kernel Function
Numerical Approximation

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
wildlife diseases
disease models
Squirrel parapoxvirus
emerging diseases

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
Spline Approximation
Volterra Integral Equations
Basis Functions
Boundary Integral Equations