Solving PDEs in C++
Numerical Methods in a Unified Object-oriented Approach. Computational Science and Engineering Series No. 1
This comprehensive book not only introduces the C and C++ programming languages but also shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach. It introduces a unified approach for the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling, where the high level of abstraction available in C++ is particularly useful, Included is all the required background in programming, PDEs, and numerical methods, and an elementary background in linear algebra and calculus. Useful exercises and solutions conclude each chapter.
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What Reviewers Are Saying
'There are dozens of excellent books on C++ and object-oriented programming, but very few of them put the language into the perspective of scientific computing. The introductory part of the present book acts as a language introduction, while the main contents focus on how C++ can be used to implement numerical algorithms. I would say that this is a long-awaited type of textbook in the scientific computing community.' Hans Petter Langtangen, Professor, Simula Research Laboratory and University of Oslo, Norway