Numerical Methods for Fluid Dynamics
This book is a major revision of Numerical Methods for Wave Equations in GeophysicalFluid Dynamics; the new title of the second editionconveysits broader scope. The second edition is designed to serve graduate students and researchers studyinggeophysical?uids, whilealso providinga non-discipline-speci?cintrod- tion to numerical methods for the solution of time-dependentdifferential equations. Changes from the ?rst edition include a new Chapter 2 on the numerical solution of ordinary differential equations (ODEs), which covers classical ODE solvers as well as more recent advances in the design of Runge–Kutta methods and schemes for the solution of stiff equations. Chapter 2 also explores several characterizations of numerical stability to help the reader distinguish between those conditions su- cient to guarantee the convergenceof numerical solutions to ODEs and the stronger stability conditions that must be satis?ed to compute reasonable solutions to ti- dependent partial differential equations with ?nite time steps. Chapter 3 (formerly Chapter 2) has been reorganized and now covers ?nite-difference schemes for the simulation of one-dimensional tracer transport due to advection, diffusion, or both.
A thorough introduction to a broad spectrum of methods of the solution of time dependent differential equations The theoretical properties of the various schemes are extensively illustrated by figures Well illustrated and includes examples and exercises throughout