Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Numerical Methods for Ordinary and Partial Differential Equations
Code MATH336
Coordinator Dr P Buividovich
Mathematical Sciences
Pavel.Buividovich@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2023-24 Level 6 FHEQ Second Semester 15

Aims

Many real-world systems in mathematics, physics and engineering can be described by differential equations. In rare cases these can be solved exactly by purely analytical methods, but much more often we can only solve the equations numerically, by reducing the problem to an iterative scheme that requires hundreds of steps. We will learn efficient methods for solving ODEs and PDEs on a computer.

Learning Outcomes

(LO1) Demonstrate an advanced knowledge of the analysis of ODEs and PDEs underpinning the scientific programming within our context.

(LO2) Demonstrate an extended understanding of scientific programming and its application to numerical analysis and to other branches of Mathematics.

(LO3) Continuous engagement with putting practical problems into mathematical language.

(S1) Numeracy

(S2) Problem solving skills

(S3) Programming skills

Syllabus
 

• Review of ODEs and PDEs
• Review of the main programming concepts needed for numerical methods: variables, conditionals, loops, arrays and procedures.
• Using Taylor expansion to derived Finite Difference Schemes.
• Euler method for ODEs.
• Runge-Kutta methods for ODEs.
• Analysis of errors, scaling.
• Numerical methods for parabolic and hyperbolic PDEs.
• Solving PDEs by relaxation and over-relaxation.
• Galerkin methods
• Finite Element Method

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
No assessment details provided  120    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 1  0    10       
Homework 2  0    10       
Canvas quizzes (self-paced)  0    20       
Homework 3  0    10