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.

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 at the end of the course. Passed laboratory course and approved assignments are also required.