Research Output per year

## 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.

1975-79 | 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 |

## 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

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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., 088190Research output: Contribution to journal › Article

Open Access

File

Galerkin Approximation

Boundary Integral

Volterra Integral Equations

Stability and Convergence

Scattering Problems