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Numerical Partial Differential Equations for Environmental Scientists and Engineers

A First Practical Course

  • Daniel R. Lynch

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. The Finite Difference Method

    1. Front Matter
      Pages 1-1
    2. Pages 3-10
    3. Pages 21-35
    4. Pages 51-87
    5. Pages 89-119
  3. The Finite Element Method

    1. Front Matter
      Pages 121-121
    2. Pages 123-137
    3. Pages 139-165
    4. Pages 189-195
    5. Pages 197-217
    6. Pages 219-261
  4. Inverse Methods

  5. Back Matter
    Pages 361-388

About this book

Introduction

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.

Keywords

calculus differential equation finite element method hyperbolic equation numerical analysis partial differential equation

Authors and affiliations

  • Daniel R. Lynch
    • 1
  1. 1.Dartmouth CollegeDartmouthUSA

Bibliographic information

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