Petr N. Vabishchevich - Böcker

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

Applied mathematical modeling is concerned with solving unsteady problems. Splitting schemes are attributed to the transition from a complex problem to a chain of simpler problems. This book shows how to construct additive difference schemes (splitting schemes) to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods) and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for systems of equations. The book is written for specialists in computational mathematics and mathematical modeling. All topics are presented in a clear and accessible manner.

In this book we describe the basic elements of present computational technologies that use the algorithmic languages C/C++. The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data. At the beginning, a brief introduction to C is given with emphasis on its easy use in scientific and engineering computations. We describe the basic elements of the language, such as variables, data types, executable statements, functions, arrays, pointers, dynamic memory and file management. After that, we present some observations on the C++ programming language. We discuss the issues of program compiling, linking, and debugging. A quick guide to Eclipse is also presented in the book. The main features for editing, compiling, debugging and application assembling are considered. As examples, we solve the standard problems of computational mathematics: operations with vectors and matrices, linear algebra problems, solution of nonlinear equations, numerical differentiation and integration, interpolation, initial value problems for ODEs and so on. Finally, basic features of computational technologies are illustrated with model problems. All programs are implemented in C/C++ with using the GSL library. Gnuplot is employed to visualize the results of computations.