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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


  • 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 Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

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.

Selected 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