This extensively updated second edition includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods, finite difference and finite elements techniques for the Poisson equation, and a variety of algorithms to solve large, sparse algebraic systems.
This extensively updated second edition includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods, finite difference and finite elements techniques for the Poisson equation, and a variety of algorithms to solve large, sparse algebraic systems.
Arieh Iserles is a Professor in Numerical Analysis of Differential Equations in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. He has been awarded the Onsager medal and served as a chair of the Society for Foundations of Computational Mathematics. He is also Managing Editor of Acta Numerica, Editor in Chief of Foundations of Computational Mathematics, and an editor of numerous other publications.
Inhaltsangabe
Preface to the first edition Preface to the second edition Flowchart of contents Part I. Ordinary Differential Equations: 1. Euler's method and beyond 2. Multistep methods 3. Runge-Kutta methods 4. Stiff equations 5. Geometric numerical integration 6. Error control 7. Nonlinear algebraic systems Part II. The Poisson Equation: 8. Finite difference schemes 9. The finite element method 10. Spectral methods 11. Gaussian elimination for sparse linear equations 12. Classical iterative methods for sparse linear equations 13. Multigrid techniques 14. Conjugate gradients 15. Fast Poisson solvers Part III. Partial Differential Equations of evolution: 16. The diffusion equation 17. Hyperbolic equations Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra A.2. Analysis Bibliography Index.
Preface to the first edition Preface to the second edition Flowchart of contents Part I. Ordinary Differential Equations: 1. Euler's method and beyond 2. Multistep methods 3. Runge-Kutta methods 4. Stiff equations 5. Geometric numerical integration 6. Error control 7. Nonlinear algebraic systems Part II. The Poisson Equation: 8. Finite difference schemes 9. The finite element method 10. Spectral methods 11. Gaussian elimination for sparse linear equations 12. Classical iterative methods for sparse linear equations 13. Multigrid techniques 14. Conjugate gradients 15. Fast Poisson solvers Part III. Partial Differential Equations of evolution: 16. The diffusion equation 17. Hyperbolic equations Appendix. Bluffer's guide to useful mathematics: A.1. Linear algebra A.2. Analysis Bibliography Index.
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