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CY905 Computational PDE's (Numerics)

This module runs within Module ES440 Computational Fluid Dynamics.

Current Lecturer:

Yongmann Chung

Current Course Homepage:

Academic Year 2014/15

Aims:

Partial differential equations arise in many areas of mathematics and several other fields such as the physics, engineering, and finance. Often these equations must be solved numerically. This module will address methods for numerically solving the most important types of partial differential equations which arise in practice.

Learning Outcomes:

  • Write a computer program to solve PDEs in one or more "space" dimensions using a finite-difference method.
  • Decide which numerical method is most appropriate to a given type of problem.
  • Appreciated concepts of stability limits and order of accuracy for numerical schemes and their relevance in programming applications.
  • Analyse a PDE problem, then produce and test program that solves the problem to within a given accuracy.

Support:

Support for this course is provided by a web based bulletin board and forum so that everyone can see them (and answer them) and so that we have an archive of questions raised. All submissions to the bulletin board are also emailed to the lecturer so she/he will see them all. Or email the lecturer directly with questions and requests for help.

ES440 and Lecture Notes

Syllabus:

 

    1. Background: Examples and classification of PDEs, nomenclature, types of flows.

    2. Forming a problem: Choice of: equations/domain/method. Uses and limitations due to stability and bounds.

    3. Difference methods: Hyperbolic and elliptic formulations, boundaries, discretisation errors, linear relaxation methods.

    4. Unsteady problems: Time-advancement of coupled ODEs, PDEs, using stability and convergence.

    5. Discretizing physical nonlinear equations.