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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
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.
Review

'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