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Solving PDEs in C++

Solving PDEs in C++
Numerical Methods in a Unified Object-Oriented Approach

textbook

Part of Computational Science and Engineering

  • Author: Yair Shapira, Technion - Israel Institute of Technology, Haifa
  • Date Published: January 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716016

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  • 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.

    • Introduces the C and C++ languages and how to use them for numerical solution of PDEs
    • Requires only an elementary background in linear algebra and calculus
    • Chapters end with exercises and solutions to aid understanding
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: January 2006
    • format: Paperback
    • isbn: 9780898716016
    • length: 184 pages
    • dimensions: 255 x 176 x 27 mm
    • weight: 0.9kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    Part I. Programming:
    1. Introduction to C
    2. Introduction to C++
    3. Data structures
    Part II. The Object-Oriented Approach:
    4. Object-oriented programming
    5. Algorithms and their object-oriented implementation
    6. Object-oriented analysis
    Part III. Partial Differential Equations and Their Discretization:
    7. The convection-diffusion equation
    8. Stability analysis
    9. Nonlinear equations
    10. Application in image processing
    Part IV. The Finite-Element Discretization Method:
    11. The weak formulation
    12. Linear finite elements
    13. Unstructured finite-element meshes
    14. Adaptive mesh refinement
    15. High-order finite elements
    Part V. The Numerical Solution of Large Sparse Linear Systems of Equations:
    16. Sparse matrices and their implementation
    17. Iterative methods for large sparse linear systems
    18. Parallelism
    Part VI. Applications:
    19. Diffusion equations
    20. The linear elasticity equations
    21. The Stokes equations
    22. Electromagnetic waves
    Appendix
    Bibliography
    Index.

  • Author

    Yair Shapira, Technion - Israel Institute of Technology, Haifa

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