This book teaches C++ and uses it to solve partial differential equations (PDEs). Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach.
The powerful features and advanced tools available in C++ are particularly useful for implementing the complex mathematical objects that are often used in numerical modeling. The code segments and their detailed explanations show how easy it is to implement advanced algorithms such as finite elements and multigrid.
The book contains such as six parts. The first two parts introduce C, C++, and the object-oriented approach. The third and fourth parts describe and implement finite-difference and finite-element schemes. The fifth part deals with numerical linear algebra and parallelism. The sixth and final part uses the present approach in advanced applications. Each chapter ends with exercises and solutions.
The book contains two theoretical chapters, which can be skipped by readers who are interested in only the practical aspects (Chapters 8 and 11 and also Sections 9.9, 12.7, 18.16, and 20.4-20.5). More advanced readers may find them most useful and relevant to the present methods.
Because the book already contains the required background in programming, PDEs, and numerical methods, the only prerequisites are calculus and linear algebra. It can thus be used as a textbook in courses on C++ for scientific computing, C++ for engineers, numerical analysis, and numerical PDEs in the advanced undergraduate and graduate levels. Because it is self-contained, it is also suitable for self-study by researchers and students in applied and computational sciences and engineering.