Numerical Methods C#

The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation (Chapter 1. 7. 6), - a solver for vibration of elastic structures (Chapter 5. 1. 6), - a step-by-step instruction of how to develop and test Diffpack programs for a physical application (Chapters 3. 6 and 3. 13), - construction of non-trivial grids using super elements (Chapters 3. 5. 4, 3. 6. 4, and 3. 13. 4), - additional material on local mesh refinements (Chapter 3. 7), - coupling of Diffpack with other types of software (Appendix B. 3) - high-level programming offinite difference solvers utilizing the new stencil (finite difference operator) concept in Diffpack (Appendix D. 8). Many of the examples, projects, and exercises from the first edition have been revised and improved.

… users on the other side of the fence … have long said that until we numerical analysts take time to write good software and get it out to the users, our ideas will not be put into action. -C.W. GEAR IN [AIKE85] This monograph is based on my doctoral thesis which I wrote dur­ ing my work at the Interdisciplinary Center for Scientific Computing (IWR) at the Ruprecht-Karls University of Heidelberg. One of my intentions was and still is to stress the practical aspects leading from the conception of mathematical methods to their effective and efficient realization as scientific software. In my own experience, I had always wished there had been something to guide me through this engineering process which accompanies the basic research for which there were nu­ merous treatises dealing, e.g., with mathematical theory for descriptor systems.

A visual, interdisciplinary approach to solving problems in numerical methods
Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++.

Although C, C++, Java, and Fortran are well-established programming languages, the relatively new C# is much easier to use for solving complex scientific and engineering problems.

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scien- tific community. Today, problems of extreme complexity can be solved. However, for real life applications, the availability of reliable scientific soft- ware seems to be emerging as a limiting factor.