Part A of this module introduces the learner to a range of technique that may be used to solve ordinary and partial differential equations. The learner will gain experience in the selection and use of the appropriate technique to solve a given equation. They will also learn to apply Monte Carlo methods to a range of physical problems.
In part B, the learner will be introduced to the principles of optimisation and how it is used. They will learn a range of different optimisation methods and how to apply those methods to physical problems.
Part A
General Runge-Kutta type methods:
- Euler
- Modified Euler
- Runge-Kutta
- Adaptive Runge-Kutta
Multistep methods
- Adams-Bashforth, Adams-Moulton
- Stiffness and multistep methods
Partial Differential equations
- Finite difference methods
- Elliptic equations
- Parabolic equations
Monte Carlo Methods
- Metropolis Algorithm
- Applications
Part B
Principles and use of optimization.
1D unconstrained optimisation
- Golden section search
- Parabolic interpolation
- Newtons method
- Brents method
- Direct and Gradient methods
Multidimensional unconstrained optimization
- Simplex method
Constrained optimization
A combination of techniques will be employed as appropriate to each element of the module content including lectures, discussion, problem-solving sessions, self learning and computational application.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 100 |