This book is a major revision of Numerical Methods for Wave Equations in Geophysical Fluid Dynamics; the new title of the second edition conveys its broader scope. The second edition is designed to serve graduate students and researchers studying geophysical fluids, while also providing a non-discipline-specific introduction to numerical methods for the solution of time-dependent differential equations. The methods considered are those at the foundation of real-world atmospheric or ocean models, with the focus being on the essential mathematical properties of each method. The fundamental character of each scheme is examined in prototypical fluid-dynamical problems like tracer transport, chemically reacting flow, shallow-water waves, and waves in an internally stratified fluid. The book includes exercises and is well illustrated with figures linking theoretical analyses to results from actual computations. Changes from the first edition include new chapters, discussions and updates throughout.From the reviews:'...The book's unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics.' Physics of Atmosphere and Ocean' excellent reference...should be brought to the attention of readers in meteorology, oceanography, physics, mechanics and excellent text book...the extensiveness, theoretical and practical extent this book reaches make it a classical work.' Acta Meteorologica Sinica

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