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## Details

Material Type: | Document, Internet resource |
---|---|

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Yair Shapira |

ISBN: | 0898716012 9780898716016 |

OCLC Number: | 213380820 |

Description: | 1 online resource (xxiii, 500 pages) : illustrations. |

Contents: | Introduction to C -- Introduction to C++ -- Data structures -- Object-oriented programming -- Algorithms and their object-oriented implementation -- Object-oriented analysis -- The convection-diffusion equation -- Stability analysis -- Nonlinear equations -- Application in image processing -- The weak formulation -- Linear finite elements -- Unstructured finite-element meshes -- Adaptive mesh refinement -- High-order finite elements -- Sparse matrices and their implementation -- Iterative methods for large sparse linear systems -- Parallelism -- Diffusion equations -- The linear elasticity equations -- The Stokes equations -- Electromagnetic waves. |

Series Title: | Computational science and engineering. |

Other Titles: | Solving partial differential equations in C++ |

Responsibility: | Yair Shapira. |

### Abstract:

This comprehensive book introduces the C and C++ programming languages and 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. 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. This book introduces a unified approach for the implementation of these objects. Solving PDEs in C++ contains all the required background in programming, PDEs, and numerical methods; only an elementary background in linear algebra and calculus is required. For the more advanced reader, there is also material on stability analysis and weak formulation. The final parts of the book demonstrate the object-oriented approach in advanced applications. Audience: researchers, engineers, and advanced students. It 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.

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