Entry requirements

Scientific computing I.

Learning outcomes

To pass, the student should be able to

• describe the fundamental concepts discretisation, accuracy and order of accuracy, efficiency, stability, discretisation errors (truncation error), ansatz, adaptivity;
• generally explain the idea behind the algorithms that are presented in the course;
• describe the fundamental difference between stochastic and deterministic algorithms;
• analyse the order of accuracy and stability properties for basic numerical methods and understand how such an analysis is employed;
• evaluate methods with respect to accuracy, stability properties and efficiency;
• based on such evaluation, discuss the suitability of methods given different different applications;
• given a mathematical model, solve problems in science and engineering by structuring the problem, choose appropriate numerical method and generate solution using software and by writing programming code;
• present, explain, summarise, evaluate and discuss solution methods and results in a short report.

Content

Continued programming in MATLAB, with specialisation in visualisation. Continued problem solving methodology. Data analysis: least squares problems with solution based on the normal equations and QR decomposition. Interpolation with an emphasis on piecewise interpolation (including cubic spines). Solution to ordinary differential equations (initial-value problem). Adaptivity. Stability. Explicit and implicit methods and in connection with this solution to non-linear equation systems. Monte Carlometoder and methods based on random number.

Instruction

Lectures, problem classes, laboratory work, compulsory assignments.

Assessment

Written examination at the end of the course and compulsory assignments.