Diccionario politécnico Beigbeder
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This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.
INDICE: I. Ordinary Differential Equations: The analytical behaviour of solutions - numerical methods for second-order boundary value problems - numerical methods for higher-order problems II. Parabolic Initial-Boundary Value Problems in One Space Dimension: Analytical behaviour of solutions - finite difference methods - finite element methods - adaptive methods III. Elliptic Boundary Value Problems: Analytical behaviour of solutions - finite difference methods - finite element methods IV. Incompressible Navier-Stokes Equations: Existence and uniqueness results - an upwind finite element method - stabilized higher order methods - adaptive error control Appendix: Robust Solvers for Linear Systems.
Numerical Analysis; Appl. Mathematics/Computational Methods of Engineering; Mathematical Biology in General. Graduate students and researchers in mathematics, natural sciences, and engineering
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