MATH4PD Numerical Solution of PDEs
Partial differential equations (PDEs) are used to model a wide range of phenomena in engineering, economics and the natural sciences. They generalise ordinary differential equations (ODEs) modelling functions of one vari- able to describe quantities depending on multiple variables, such as time and space, or several spatial dimensions. Examples are the heat equation, the Laplace equa- tion and the wave equation. Because closed-form analytical solutions can seldom be found, even for the simplest PDEs, approximate solutions are usually sought. This course gives an overview of approximation methods for solving PDEs on finite domains, the so-called boundary-value problems, ranging from the semi-analytical separation of variable technique to the numerical finite difference method. The focus of the paper will be on implementing methods to generate approximate solu- tions using computational software Matlab and analyse their properties.
The following topics will covered
- Separation of variables
- Finite difference method
- Method of lines
- Spectral methods
- Finite element method (if time permits)
2018, Semester 1.
MATH202 and MATH203. COMO204, COMO303 and MATH304 are recommended. Some experience using the computational software Matlab would be helpful.
Fabien Montel (email@example.com).
Your final mark F in the paper will be calculated according to this formula:
F = max(E, (4E + A + P)/6)
- E is the Exam mark
- A is the Assignments mark
- P is the Project mark
and all quantities are expressed as percentages.
Students must abide by the University’s Academic Integrity Policy
Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.
The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.
Academic misconduct: Plagiarism
Plagiarism is defined as:
- Copying or paraphrasing another person’s work and presenting it as your own.
- Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
- Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
- Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.
All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.
Academic misconduct: Unauthorised Collaboration
Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.