Modern Methods in Scientific Computing and Applications

The influence of scientific computing widened considerably in almost every area during the last few decades of the 20th century. Science and engineering particularly are areas greatly influenced by simulations - image processing, thin films, mathematical finance, electrical engineering, moving interfaces and combustion rely on the field, to name but a few. One half of this book focuses on the techniques of scientific computing: domain decomposition, the absorption of boundary conditions and one-way operators, convergence analysis of multi-grid methods and other multi-grid techniques, dynamical systems, and matrix analysis. The remainder of the book is concerned with combining techniques with concrete applications: stochastic differential equations, image processing, thin films, and asymptotic analysis for combustion problems.