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
- Co-Director, Mathematical Modelling, Analysis and Computation - Maxwell Institute Graduate School (MAC-MIGS), an EPSRC Centre for Doctoral Training
- Trustee, James Clerk Maxwell Foundation
Teaching:
- SMSTC Applied Mathematics Methods (for PhD students), Numerical ODEs.
Previous Roles:
- Head of Department of Mathematics
- Deputy Director, Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), an EPSRC/SFC Centre for Doctoral Training
- 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.
| 1975-79 | St Andrews University, BSc in Applied Mathematics. |
| 1979-82 | Dundee Univeristy, PhD in numerical analysis |
| 1982-86 | Atomic Energy of Canada Ltd., mathematician and numerical analyst |
| 1986- | Heriot-Watt University, Department of Mathematics |
Expertise related to UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This person’s work contributes towards the following SDG(s):
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SDG 3 Good Health and Well-being -
SDG 7 Affordable and Clean Energy
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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 journal › Article › peer-review
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Positivity of a weakly singular operator and approximation of wave scattering from the sphere
Duncan, D. B., 2 Dec 2022, In: Journal of Integral Equations and Applications. 34, 3, p. 317-333 17 p.Research output: Contribution to journal › Article › peer-review
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Finite-dimensional coagulation-fragmentation dynamics
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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 journal › Article › peer-review
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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 journal › Article › peer-review
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