This book surveys the most recent research in six key areas related to numerical solutions of differential equations. It covers guaranteed error bounds for ordinary differential equations; an introduction to computational methods for differential equations; numerical solution of differential-algebraic equations, boundary element methods; and perturbation theory for infinite dimensional dynamical systems. It draws together a method that is currently journals, introducing the reader to important current research. This book is written at a level for graduate students and researchers in computational mathematics and in application areas in physics and engineering. This book is intended for research in computational mathematics and in its application area in physics and engineering.
This book surveys the most recent research in six key areas related to numerical solutions of differential equations. It covers guaranteed error bounds for ordinary differential equations; an introduction to computational methods for differential equations; numerical solution of differential-algebraic equations, boundary element methods; and perturbation theory for infinite dimensional dynamical systems. It draws together a method that is currently journals, introducing the reader to important current research. This book is written at a level for graduate students and researchers in computational mathematics and in application areas in physics and engineering. This book is intended for research in computational mathematics and in its application area in physics and engineering.
George F. Corliss: Guaranteed Error Bounds for Ordinary
Differential Equations
Kenneth Eriksson, Don Estap, Peter Hansbo and Claes Johnson:
Introduction to Computational Methods for Differential
Equations
Linda R. Petzold: Numerical Solution of Differential-Algebraic
Equations
Ian H. Sloan: Boundary Element Methods
Andrew Stuart: Perturbation Theory for Infinite Dimensional
Dynamical Systems
M. Zennaro: Delay Differential Equations: Theory and Numerics
`A particularly appealing aspect of this work is the basic uniform
methodology for elliptic as well as time-dependent parabolic and
hyperbolic PDE's. Much of this material is relatively new having
been developed in the last several years'
Mathematics of Computation Vol. 66
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