Numerical Partial Differential Equations For Environmental Scientists And Engineers
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Numerical Partial Differential Equations for Environmental Scientists and Engineers
Author: Daniel R. Lynch
language: en
Publisher: Springer Science & Business Media
Release Date: 2004-12-15
For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.
Numerical Partial Differential Equations for Environmental Scientists and Engineers
Author: Daniel R. Lynch
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-06-02
This book concerns the practical solution of Partial Differential Equations. We assume the reader knows what a PDE is - that he or she has derived some, and solved them with the limited but powerful arsenal of analytic techniques. We also assume that (s)he has gained some intuitive knowledge of their solution properties, either in the context of specific applications, or in the more abstract context of applied mathematics. We assume the reader now wants to solve PDE's for real, in the context of practical problems with all of their warts - awkward geometry, driven by real data, variable coefficients, nonlinearities - as they arise in real situations. The applications we envision span classical mathematical physics and the "engineering sciences" : fluid mechanics, solid mechanics, electricity and magnetism, heat and mass transfer, wave propagation. Of course, these all share a joyous interdisciplinary unity in PDE's. The material arises from lectures at Dartmouth College for first-year graduate students in science and engineering. That audience has shared the above motivations, and a mathematical background including: ordinary and partial differential equations; a first course in numerical an- ysis; linear algebra; complex numbers at least at the level of Fourier analysis; and an ability to program modern computers. Some working exposure to applications of PDE's in their research or practice has also been a common denominator. This classical undergraduate preparation sets the stage for our "First Practical Course". Naturally, the "practical" aspect of the course involves computation.
Numerical Methods for Solving Partial Differential Equations
Author: George F. Pinder
language: en
Publisher: John Wiley & Sons
Release Date: 2018-02-05
A comprehensive guide to numerical methods for simulating physical-chemical systems This book offers a systematic, highly accessible presentation of numerical methods used to simulate the behavior of physical-chemical systems. Unlike most books on the subject, it focuses on methodology rather than specific applications. Written for students and professionals across an array of scientific and engineering disciplines and with varying levels of experience with applied mathematics, it provides comprehensive descriptions of numerical methods without requiring an advanced mathematical background. Based on its author’s more than forty years of experience teaching numerical methods to engineering students, Numerical Methods for Solving Partial Differential Equations presents the fundamentals of all of the commonly used numerical methods for solving differential equations at a level appropriate for advanced undergraduates and first-year graduate students in science and engineering. Throughout, elementary examples show how numerical methods are used to solve generic versions of equations that arise in many scientific and engineering disciplines. In writing it, the author took pains to ensure that no assumptions were made about the background discipline of the reader. Covers the spectrum of numerical methods that are used to simulate the behavior of physical-chemical systems that occur in science and engineering Written by a professor of engineering with more than forty years of experience teaching numerical methods to engineers Requires only elementary knowledge of differential equations and matrix algebra to master the material Designed to teach students to understand, appreciate and apply the basic mathematics and equations on which Mathcad and similar commercial software packages are based Comprehensive yet accessible to readers with limited mathematical knowledge, Numerical Methods for Solving Partial Differential Equations is an excellent text for advanced undergraduates and first-year graduate students in the sciences and engineering. It is also a valuable working reference for professionals in engineering, physics, chemistry, computer science, and applied mathematics.