Numerical Methods for Evolutionary Differential Equations
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Author(s): U. M. Ascher
Publisher: SIAM
ISBN: 9780898716528
Format: softback
395pp
Price: $79.00
Review Date: 20 August 2008
Review: There is an increasing demand for efficient methods for numerical simulation of dynamic mathematical models. Mathematical models involving evolutionary partial differential equations as well as ordinary differential equations (ODE) occur in many applications, such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finances. Therefore this text book emphasises the study of principles, properties and use of numerical methods, from the viewpoint of applicability. There are chapters on: Methods and concepts of ODEs; Finite difference and finite volume methods; Stability for constant coefficient problems; Hamiltonian systems and long-time integration; Dispersion and dissipation; Handling boundary conditions; Several space variables and splitting methods; Discontinuities and almost discontinuities; and Additional topics (nonuniform meshes, level set methods).