Introduction to Numerical Modeling in the Earth Sciences
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Product details:
- Publisher OUP Oxford
- Date of Publication 10 July 2025
- ISBN 9780198802716
- Binding Hardback
- No. of pages272 pages
- Size 246x189 mm
- Language English
- Illustrations 77 b/w and colour images 700
Categories
Short description:
This textbook offers a concise but self-contained introduction to the art of numerical modelling in sciences. It discusses all the steps, from the mathematical foundations of the model to the solution procedures that are commonly used by advanced practitioners.
MoreLong description:
This textbook provides an introduction to the world of numerical modeling in the physical sciences, focusing more specifically on earth and planetary sciences. It is designed to lead the reader through the process of defining the mathematical or physical model of interest and applying numerical methods to approximate and explore the solutions to these models, while also providing a quantitative assessment of the limitations, performance and quality of these approximations.
The book is designed to provide a self-contained reference by including the mathematical foundations required to understand the models and their convergence. It includes a detailed discussion of models for ordinary systems of equation and partial differential equations, with pseudo-codes detailing the solution procedure. Examples are drawn from the fields of earth and planetary sciences, including, geochemical box models, non-linear ordinary differential equations describing the evolution of subvolcanic magma chambers, the mass conservation of cosmogenic nuclides in soils, diffusion in minerals, the hillslope equation, the advection-diffusion and wave equations and the shallow water equations.
Featuring numerous examples drawn from earth and planetary sciences, the content of this book has been used by the author to teach numerical methods classes at the undergraduate and graduate levels over several years, and will provide an excellent resources for teachers and learners in this area.
Table of Contents:
Part I - Mathematical concepts
Introduction to real valued calculus
Introduction to multivariate calculus
Elements of complex calculus
Elements of linear algebra
Treating functions as vectors
Ordinary Differential Equations (ODEs)
Partial Differential Equations (PDEs)
Part II - Numerical Modeling, Ordinary Differential Equations (ODEs)
First order ODE (time integration): The nuclear decay equation as a starting point
What controls convergence? What relates convergence and stability?
Box Models: from single to multiple coupled ODEs
Higher order ODEs
Higher order discretization methods
Part III - Numerical Modeling, Partial Differential Equations (PDEs)
Important mathematical notions when working with PDEs
Von Neumann stability analysis: concepts
1-D advection equation
Diffusion equation
1-D advection-diffusion equation
1-D wave equation
The shallow water equation
Part IV - Overview of other numerical methods
Top-down approaches
Bottom-up approaches
Introduction to Numerical Modeling in the Earth Sciences
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