Syllabus for Analysis of Numerical Methods

Analys av numeriska metoder

Syllabus

  • 5 credits
  • Course code: 1TD243
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Computer Science A1F, Technology A1F, Computational Science A1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle
    G1N: has only upper-secondary level entry requirements
    G1F: has less than 60 credits in first-cycle course/s as entry requirements
    G1E: contains specially designed degree project for Higher Education Diploma
    G2F: has at least 60 credits in first-cycle course/s as entry requirements
    G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    GXX: in-depth level of the course cannot be classified.

    Second cycle
    A1N: has only first-cycle course/s as entry requirements
    A1F: has second-cycle course/s as entry requirements
    A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    AXX: in-depth level of the course cannot be classified.

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2011-03-10
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2011-03-10
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 20, 2013
  • Entry requirements: 120 credits of which at least 60 credits in mathematics (linear algebra, vector calculus, complex analysis, Fourier analysis must be covered), Computer Programming I and Scientific Computing III or the equivalent is included.
  • Responsible department: Department of Information Technology

Learning outcomes

To pass, the student should be able to

  • analyse linear systems of partial differential equations;
  • analyse finite difference approximations of systems of partial differential equations;
  • analyse nonlinear partial differential equations and finite difference equations;
  • apply the methodology in Finite difference methods, Finite Volume methods, Spectralmethods and the Fast Fourier Transform (FFT);
  • choose and implement suitable numerical methods for solving scientific and engineering problems described by partial differential equations;
  • interpret, analyse and evaluate numrical methods and numerical results.

Content

Basic properties of numerical methods for partial differential equations: consistency, convergence,s tability, efficiency. Applying stability theory for multi-step and Runge-Kutta methods on initial value problems for ordinary differential equations. Fourier methods for analysing stability, dissipation and dispersion of finite difference methods for linear hyperbolic and parabolic systems with periodic boundary conditions. Energy methods for analysing stability and well-posedness for simple initial-boundary-value problems and corresponding finite difference methods. Analysing properties of non-linear scalar partial differential equations and corresponding finite difference methods, such as hyperbolicity, parabolicity, Rankine-Hugoniot condition, conservation, total variation diminishing. Spectral methods, Finite Volume methods and fast Fourier transform (FFT).

Instruction

Lectures, problem solving classes and compulsory assignments.

Assessment

Written exam (3 credits) and approved assignments (2 credits) .

Syllabus Revisions

Reading list

Reading list

Applies from: week 14, 2013

Some titles may be available electronically through the University library.

  • Gustafsson, Bertil. High order difference methods for time dependent PDE

    1st ed.: New York: Springer, cop. 2008

    Find in the library

    Mandatory

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