This module starts by reviewing the Newton solver in 1D and 2D. Linear and non-linear equation solving methods are briefly touched upon before the basics of solving an Ordinary Differential Equation (implicit and explicit Euler methods) are discussed. The method of lines for solving Differential Algebraic Equations (DAEs) is explained. Discretization (finite difference, finite element and finite volume), orders of approximation and number of points are all discussed. Round-off and truncation errors are explained. Numerical dispersion, high-index problems and scaling are also covered.
At the end of this module, students should have a grasp of what numerical techniques are used in solving DAE systems, how to select discretization method, order and number of points. They should have a basic understanding of numerical artifacts such as high-index problems, scaling etc.
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|Home Assignment -LNG tank truck||DOCX|
|Home Assignment- Rocket to the moon||DOCX|
|Numerical Solutions slides||PPTX|
|Home Assignment -LNG tank truck|
|Home Assignment -Rocket to the moon|
|Numerical Solutions slides|