Van Kan J. Numerical Methods in Scientific Computing 2023

Textbook in PDF format

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. Their aim is to show the place of numerical solutions in the general modeling process and this 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 aims especially 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. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.
Preface.
Review of some basic mathematical concepts.
A crash course in PDE’s.
Finite difference methods.
Finite volume methods.
Minimization problems in physics.
The numerical solution of minimization problems.
The weak formulation and Galerkin’s method.
Extension of the FEM.
Solution of large systems of equations.
The heat- or diffusion equation.
The wave equation.
The transport equation.
Moving boundary problems