Numerical Methods in Scientific Computing
This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. The aim is to show the place of numerical solutions in the general modeling process, which must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account, especially for validation of the numerical solution obtained.
This book in other words is especially aimed at engineers and scientists who have 'real world' problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background.
2 A Crash Course in PDE's
3 Finite Difference Methods
4 Finite Volume Methods
5 Minimization Problems in Physics
6 The Numerical Solution of Minimization Problems
7 The Weak Formulation and Galerkin's Method
8 Extension of the FEM
9 Solution of large systems of equations
10 The heat- or diffusion equation
11 The wave equation
12 The transport equation
13 Moving boundary problems