URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=4MC10&collegejaar=2025&taal=enDescription
Mathematical models used in engineering often take the form of ordinary or partial differential equations. In most practical cases, these equations cannot be solved analytically and one thus has to resort to numerical, approximate solutions. Numerical solutions are generally constructed by discretising the differential equation in space and/or time. Two common methods used for this purpose are the finite difference method and finite element method. The former directly replaces derivatives in the equation to be solved by difference quotients, whereas the latter introduces interpolation in the so-called weak form of the equation. Both methods ultimately result in a system of (linear or nonlinear) algebraic equations which are well suited for implementation in computer codes.This course focusses on differential equations encountered in fluid dynamics and solid mechanics. It aims to comprehensively treat the translation of these differential equations into algorithms – and in fact all the way into computer code. Emphasis is on the underlying theory and on the approximations made to render the problem tractable – including e.g. numerical quadrature. Attention is furthermore paid to concepts such as convergence, discretisation error etc., as well as to algorithms to construct and solve the resulting algebraic equations. In examples and exercises the methods are implemented in relatively straightforward Matlab programs. This should prepare the student optimally to responsibly use commercial software or, where necessary, to develop a purpose-built code.