# Module Overview

### Numerical Analysis

The aim of this module is to equip the learner with the knowledge necessary to effectively select and implement finite-difference methods for the numerical integration of differential equations.

During the first part of the module the learner will be introduced to the theory and practice of common techniques for the numerical integration of ordinary differential equations with initial conditions.

The second part of the module will focus on numerical methods for partial differential equations.

iPython notebooks (or equivalent) will be used to implement numerical methods.

MATH 4806

##### ECTS Credits

5

*Curricular information is subject to change

Ordinary Differential Equations Linear systems; Finite-differencing techniques; Stability analysis; Explicit Runge-Kutta methods; Adaptive stepsize control, Convergence analysis.

Boundary Value Problems: Shooting method, non-linear shooting method, finite difference schemes,

Partial Differential Equations; Finite-differencing;

Parabolic Equations: Heat equation; Crank-Nicolson method, implicit and explicit methods

Hyberbolic Equations: Advection equation; Courant Friedrichs Lewy condition

Elliptic Equations: Poisson equation, five point scheme.

Ordinary Differential Equations Linear systems

Finite-differencing techniques; Stability analysis; Explicit Runge-Kutta methods; Adaptive stepsize control, Convergence analysis.Boundary Value Problems: Shooting method, non-linear shooting method, finite difference schemes.

Partial Differential Equations; Finite-differencing

Parabolic Equations: Heat equation; Crank-Nicolson method, implicit and explicit methodsHyberbolic Equations: Advection equation; Courant Friedrichs Lewy conditionElliptic Equations: Poisson equation, five point scheme.

The module will be delivered through lectures and tutorials. This will be supplemented with time in the computer laboratory.

In addition, students will be required to undertake background reading and self-directed learning. Modules are also typically supported by tutorial sheets, example classes and, laboratory sessions. The self-directed learning hours will be devoted to preparing for lectures, undertaking solutions to example sheets, reflecting upon the lecture material, refining and deepening understanding and consolidating individual learning. Modules may be supported by online material and delivery and computer laboratory sessions. Where online delivery takes place this may substitute for some contact hours.

Module Content & Assessment
Assessment Breakdown %
Formal Examination75
Other Assessment(s)25