Advanced Numerical Analysis (L.7) (852G1)
Advanced Numerical Analysis (L.7)
Module 852G1
Module details for 2023/24.
15 credits
FHEQ Level 7 (Masters)
Module Outline
Iterative methods for linear systems: Jacobi and Gauss-Seidel, conjugate gradient, GMRES, Krylov Methods
Iterative methods for nonlinear systems: fixed point iteration, Newton's method, Inexact Newton
Optimisation: simplex methods, descent methods, convex optimisation, non-convenx optimisation
Eigenvalue problems: power method, Von Mises method, Jacobi iteration, special matrices
Numerical methods for ordinary differential equations: existence of solutions for ODE's, Euler's method, Lindelöf-Picard method, continuous dependence and stability of ODE's, basic methods: forward and backward Euler, stability, convergence, midpoint and trapezoidal methods: order of convergence, truncation error, stability convergence, absolute stability, A-stability
Runge-Kutta methods: one step methods, predictor-corrector methods, explicit RK2 and RK4 as basic examples, general theory of RK methods: truncation, consitency, stability, convergence
Linear Multistep methods: multistep methods, truncation,consistency, stability, convergence, difference equaitons, Dahlquist's barriers, Adams family, backward difference formulas
Boundary value problems in 1d, shooting methods, finite difference methods, convergence analysis, Galerkin methods, convergence analysis
Module learning outcomes
Analyse in depth the convergence properties of advanced iterative methods
Implement and apply advanced iterative methods to solve linear and nonlinear problems
Analyse in depth the convergence and stability properties of advanced time-stepping methods
Conduct thorough error analysis
Implement and apply time-stepping methods to solve ODE's and time-dependent PDE's including boundary value problems
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T1 Week 11 | 35.00% |
| Problem Set | T1 Week 10 | 10.00% |
| Problem Set | T1 Week 8 | 10.00% |
| Problem Set | T1 Week 5 | 10.00% |
| Project | T1 Week 11 | 35.00% |
| Unseen Examination | Semester 1 Assessment | 80.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Semester | Lecture | 2 hours | 11111111111 |
| Autumn Semester | Lecture | 1 hour | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Omar Lakkis
Assess convenor, Convenor
/profiles/173323
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