Computational Differential Equations (MAST90026)

Graduate courseworkPoints: 12.5Not available in 2025

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Overview

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Many processes in the natural sciences, engineering and finance are described mathematically using ordinary or partial differential equations. Only the simplest or those with special structure can be solved exactly. This subject discusses common techniques for computing numerical solutions to differential equations and introduces the major themes of accuracy, stability and efficiency. Understanding these basic properties of scientific computing algorithms should prevent the unwary from using software packages inappropriately or uncritically, and provide a foundation for devising methods for nonstandard problems. We cover both time-independent problems, in one and higher space dimensions, and evolution equations of hyperbolic or parabolic type.

Intended learning outcomes

After completing this subject, students should:




 

 

 

  • appreciate how and why numerical methods are developed to solve differential equations commonly arising in finance, science and engineering;
  • understand the chief factors to be considered in choosing an appropriate algorithm for a given class of problem;
  • acquire high level numerical tools and knowledge that can be used to solve a range of problems in science and engineering;
  • gain the ability to pursue further studies in this and related areas.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 4 March 2025

Eligibility and requirements

Prerequisites

Students should be able to program in one of: C, Matlab, Mathematica, Perl, Fortran, Python etc

Corequisites

None

Non-allowed subjects

None

Recommended background knowledge


Students are required to write programs in MATLAB so previous experience in writing and debugging procedural computer programs is expected. It is recommended that students have completed a subject in partial differential equations.

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 4 March 2025

Assessment

DescriptionTimingPercentage

Weekly homework for the first four weeks

Early in the teaching period20%

Up to 60 pages of written assignments (three assignments worth 20% each due mid and late in semester)

  • 60 pages
Second half of the teaching period60%

An oral presentation on a project held towards the end of semester

  • 15 minutes
Second half of the teaching period20%

Last updated: 4 March 2025

Dates & times

Not available in 2025

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  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Last updated: 4 March 2025

Further information

  • Texts

    Prescribed texts

    TBA

    Recommended texts and other resources

    R.J.Leveque, Finite difference methods for ordinary and partial differential equations. Steady-state and time-dependent problems, SIAM, 2007.
    A. Iserles, A First Course in the Numerical Analysis of Differential Equations, 2nd edn, Cambridge University Press, 2008.

  • Related Handbook entries

    This subject contributes to the following:

    TypeName
    CoursePh.D.- Engineering
    CourseMaster of Science (Mathematics and Statistics)
    CourseDoctor of Philosophy - Engineering
    CourseMaster of Philosophy - Engineering
    Informal specialisationMathematics and Statistics
  • Available through the Community Access Program

    About the Community Access Program (CAP)

    This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

    Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants

    Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.

  • Available to Study Abroad and/or Study Exchange Students

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 4 March 2025