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). Included is all the required background in programming, PDEs, numerical methods, linear algebra and calculus. Useful exercises and solutions conclude each chapter.
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). Included is all the required background in programming, PDEs, numerical methods, linear algebra and calculus. Useful exercises and solutions conclude each chapter.
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.
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.
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