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Solving PDEs in C++: Numerical Methods in a Unified Object-Oriented Approach, Second Edition

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by Yair Shapira


2012 / xxxii + 776 / Softcover / ISBN 978-1-611972-16-0 / List Price $148.00 / SIAM Member Price $103.60 / Order Code CS09

Keywords: PDE, C++, object-oriented programming, numerical method

Sample Chapter

Original Code - Compile with GNU

"The present book therefore devotes more than 150 pages to introduce the reader to object oriented program development. In this vein, the languages C and C++ are exposed as are data structures and principles of object oriented programming. This is accomplished in a thoughtful way . . . . An essential part concerns the proper dealing with the meshes, including mesh refinement. . . . Once the reader has mastered the material, he will be in a good position to construct proper models, discretize the equation, and develop a professional code for quite a number of problems."
    - H. Muthsam, Wien
      Monatsch Math (2014) 174:163–168

In this much-expanded second edition, author Yair Shapira presents new applications and a substantial extension of the original object-oriented framework to make this popular and comprehensive book even easier to understand and use. It 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). The complete code is available and explained in detail in the text or the appendix, tested on GNU, and easily adapted to other compilers as well.

New material in this edition includes

  • new chapters on 3-D nonlinear applications and image processing applications;
  • new sections on cryptography applications; and
  • even more new sections, many including additional algorithms.

The book leads readers through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The high level of abstraction available in C++ is particularly useful in the implementation of complex mathematical objects, such as unstructured mesh, sparse matrix, and multigrid hierarchy, often used in numerical modeling. The well-debugged and tested code segments implement the numerical methods efficiently and transparently in a unified object-oriented approach.

The book is written for researchers, engineers, and advanced students who wish to increase their familiarity with numerical methods and to implement them using modern programming tools. Solving PDEs in C++ can be used as a textbook in courses in C++ with applications, C++ in engineering, numerical analysis, and numerical PDEs at the advanced undergraduate and graduate levels. Because it is self-contained, the book is also suitable for self-study by researchers and students in applied and computational science and engineering.

About the Author
Yair Shapira is engaged in research in the Computer Science Department, Technion-Israel Institute of Technology, Haifa, Israel. His main research interests are multigrid, preconditioning, and numerical methods. He is author of the books Matrix-Based Multigrid: Theory and Applications, Second Edition (Springer, 2008) and Mathematical Objects in C++: Computational Tools in a Unified Object-Oriented Approach (CRC, 2009).

This second edition replaces Solving PDEs in C++: Numerical Methods in a Unified Object-Oriented Approach (CS01, 978-0-898716-01-6), which is no longer available.

ISBN 9781611972160

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