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Earth Sciences & Geography | Numerical Partial Differential Equations for Environmental Scientists and… - A First Practical

Numerical Partial Differential Equations for Environmental Scientists and Engineers

A First Practical Course

Lynch, Daniel R.

2005, XXIV, 388 p.

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This book concerns the practical solution of Partial Differential Equations (PDEs). It reflects an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It assumes the reader has gained some intuitive knowledge of PDE solution properties and now wants to solve some for real, in the context of practical problems arising in real situations. The practical aspect of this book is the infused focus on computation. It presents two major discretization methods – Finite Difference and Finite Element. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems. It is divided into three parts. Part I is an overview of Finite Difference Methods. Part II focuses on Finite Element Methods, including an FEM tutorial. Part III deals with Inverse Methods, introducing formal approaches to practical problems which are ill-posed.

Content Level » Graduate

Keywords » calculus - differential equation - finite element method - hyperbolic equation - numerical analysis - partial differential equation

Related subjects » Civil Engineering - Computational Intelligence and Complexity - Earth Sciences & Geography

Table of contents / Sample pages 

The Finite Difference Method.- Introduction.- Finite Difference Calculus.- Elliptic Equations.- Elliptic Iterations.- Parabolic Equations.- Hyperbolic Equations.- The Finite Element Method.- General Principles.- A 10D Tutorial.- Multi-Dimensional Elements.- Time-Dependent Problems.- Vector Problems.- Numerical Analysis.- Inverse Methods.- Inverse Noise, SVD, and LLS.- Fitting Models to Data.- Dynamic Inversion.- Time Conventions for Real-Time Assimilation.- Skill Assessment for Data Assimilative Models.- Statistical Interpolation.- Appendices.- Bibliography.- Index.

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