A First Course In The Numerical Analysis Of Differential Equations [Book News & Reviews]

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for realnumber calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis both of ordinary and partial differential equations. The point of departure is mathematical, but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. This new edition has been extensively updated, and includes new chapters on developing subject areas: geometric numerical integration, an emerging paradigm for numerical computation that exhibits exact conservation of important geometric and structural features of the underlying differential equation; spectral methods, which have come to be seen in the last two decades as a serious competitor to finite differences and finite elements; and conjugate gradients, one of the most powerful contemporary tools in the solution of sparse linear algebraic systems. Other topics covered include numerical solution of ordinary differential equations by multistep and Runge–Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques for their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.