Numerical Methods for Solving Partial Differential Equations A Comprehensive Introduction for Scientists and Engineers 1st Edition by George Pinder ISBN 9781119316381 1119316383

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Product details:
ISBN 10: 1119316383
ISBN 13: 9781119316381
Author: George Pinder

 

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.

Numerical Methods for Solving Partial Differential Equations A Comprehensive Introduction for Scientists and Engineers 1st Edition Table of contents:

Chapter 1: Interpolation

1.1 Purpose

1.2 Definitions

1.3 Example

1.4 Weirstraus Approximation Theorem

1.5 Lagrange Interpolation

1.6 Compare and

1.7 Error of Approximation

1.8 Multiple Elements

1.9 Hermite Polynomials

1.10 Error in Approximation by Hermites

1.11 Chapter Summary

1.12 Problems

Bibliography

Chapter 2: Numerical Differentiation

2.1 General Theory

2.2 Two‐Point Difference Formulae

2.3 Two‐Point Formulae from Taylor Series

2.4 Three‐point Difference Formulae

2.5 Chapter Summary

2.6 Problems

Bibliography

Note

Chapter 3: Numerical Integration

3.1 Newton‐Cotes Quadrature Formula

3.2 Chapter Summary

3.3 Problems

Bibliography

Chapter 4: Initial Value Problems

4.1 Euler Forward Integration Method Example

4.2 Convergence

4.3 Consistency

4.4 Stability

4.5 Lax Equivalence Theorem

4.6 RungeKutta Type Formulae

4.7 Chapter Summary

4.8 Problems

Bibliography

Note

Chapter 5: Weighted Residuals Methods

5.1 Finite Volume or Subdomain Method

5.2 Galerkin Method for First Order Equations

5.3 Galerkin Method for Second‐Order Equations

5.4 Finite Volume Method for Second‐Order Equations

5.5 Collocation Method

5.6 Chapter Summary

5.7 Problems

Bibliography

Chapter 6: Initial Boundary‐Value Problems

6.1 Introduction

6.2 Two Dimensional Polynomial Approximations

6.3 Finite Difference Approximation

6.4 Stability of Finite Difference Approximations

6.5 Galerkin Finite Element Approximations in Time

6.6 Chapter Summary

6.7 Problems

Bibliography

Chapter 7: Finite Difference Methods in Two Space

7.1 Example Problem

7.2 Chapter Summary

7.3 Problems

Bibliography

Chapter 8: Finite Element Methods in Two Space

8.1 Finite Element Approximations over Rectangles

8.2 Finite Element Approximations over Triangles

8.3 Isoparametric Finite Element Approximation

8.4 Chapter Summary

8.5 Problems

Bibliography

Chapter 9: Finite Volume Approximation in Two Space

9.1 Finite Volume Formulation

9.2 Finite Volume Example Problem 1

9.3 Finite Volume Example Problem Two

9.4 Chapter Summary

9.5 Problems

Bibliography

Chapter 10: Initial Boundary‐Value Problems

10.1 Mass Lumping

10.2 Chapter Summary

10.3 Problems

Bibliography

Chapter 11: Boundary‐Value Problems in Three Space

11.1 Finite Difference Approximations

11.2 Finite Element Approximations

11.3 Chapter Summary

Bibliography

Chapter 12: Nomenclature

Index

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