The book provides the mathematical basis for investigating numerical equations from physics, life sciences or engineering. Tools for analysis and algorithms are applied to a large set of relevant examples to show the difficulties and the limitations of the most naïve approaches. Not only do these examples give the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail through the mathematical perspective.
Chapter 1 addresses the solution of ordinary differential equations, and includes an overview of its essential theoretical basis. The analysis of classical schemes is also covered, and various concepts of stability are illustrated primarily by the description of biological systems. Chapter 2 deals with numerical solutions to elliptic boundary value problems, as well as techniques related to optimization. The final chapter concentrates on evolutionary partial differential equations, looking at questions of stability and consistency for the heat equation and for hyperbolic problems.
1. Ordinary Differential Equations.
2. Numerical Simulation of Stationary Partial Differential Equations: Elliptic Problems.
3. Numerical Simulations of Partial Differential Equations:Time-dependent Problems.
Thierry Goudon is Senior Research Scientist at Université Côte d’Azur (Inria, CNRS, LJAD) in France. His research is mainly motivated by the analysis and numerical simulation of partial differential equations arising in physics.
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