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Numerical Methods in Engineering & Science

This book is designed for an introductory course in numerical methods for students of engineering and science at universities and colleges of advanced education. It is an outgrowth of a course of lectures and tutorials (problem­ solving sessions) which the author has given for a number of years at t...

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Bibliographic Details
Other Authors: Davis, Graham de Vahl (Editor)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1986, 1986
Edition:1st ed. 1986
Subjects:
Humanities And Social Sciences
Humanities
Social Sciences
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 6.11 Higher-order equations 238 Problems
  • 7 Partial differential equations II — parabolic equations
  • 7.1 Introduction
  • 7.2 The conduction equation
  • 7.3 Non-dimensional equations yet again
  • 7.4 Notation
  • 7.5 An explicit method
  • 7.6 Consistency
  • 7.7 The Dufort-Frankel method
  • 7.8 Convergence
  • 7.9 Stability
  • 7.10 An unstable finite difference approximation
  • 7.11 Richardson’s extrapolation 261 Worked examples 262 Problems
  • 8 Integral methods for the solution of boundary value problems
  • 8.1 Introduction
  • 8.2 Integral methods
  • 8.3 Implementation of integral methods 271 Worked examples 278 Problems
  • Suggestions for further reading
  • 3.8 Iterative methods for linear systems
  • 3.9 Matrix inversion
  • 3.10 The method of least squares
  • 3.11 The method of differential correction
  • 3.12 Simple iteration for non-linear systems
  • 3.13 Newton’s method for non-linear systems
  • Worked examples
  • Problems
  • 4 Interpolation, differentiation and integration
  • 4.1 Introduction
  • 4.2 Finite difference operators
  • 4.3 Difference tables
  • 4.4 Interpolation
  • 4.5 Newton’s forward formula
  • 4.6 Newton’s backward formula
  • 4.7 Stirling’s central difference formula
  • 4.8 Numerical differentiation
  • 4.9 Truncation errors
  • 4.10 Summary of differentiation formulae
  • 4.11 Differentiation at non-tabular points: maxima and minima
  • 4.12 Numerical integration
  • 4.13 Error estimation
  • 4.14 Integration using backward differences
  • 4.15 Summary of integration formulae
  • 4.16 Reducing the truncationerror 146 Worked examples 149 Problems
  • 5 Ordinary differential equations
  • 5.1 Introduction
  • 5.2 Euler’s method
  • 5.3 Solution using Taylor’s series
  • 5.4 The modified Euler method
  • 5.5 Predictor-corrector methods
  • 5.6 Milne’s method, Adams’ method, and Hamming’s method
  • 5.7 Starting procedure for predictor-corrector methods
  • 5.8 Estimation of error of predictor-corrector methods
  • 5.9 Runge-Kutta methods
  • 5.10 Runge-Kutta-Merson method
  • 5.11 Application to higher-order equations and to systems
  • 5.12 Two-point boundary value problems
  • 5.13 Non-linear two-point boundary value problems 198 Worked examples 199 Problems
  • 6 Partial differential equations I — elliptic equations
  • 6.1 Introduction
  • 6.2 The approximation of elliptic equations
  • 6.3 Boundary conditions
  • 6.4 Non-dimensional equations again
  • 6.5 Method of solution
  • 6.6 The accuracy of the solution
  • 6.7 Use of Richardson’s extrapolation
  • 6.8 Other boundary conditions
  • 6.9 Relaxation by hand-calculation
  • 6.10 Non-rectangular solution regions
  • 1 Introduction
  • 1.1 What are numerical methods?
  • 1.2 Numerical methods versus numerical analysis
  • 1.3 Why use numerical methods?
  • 1.4 Approximate equations and approximate solutions
  • 1.5 The use of numerical methods
  • 1.6 Errors
  • 1.7 Non-dimensional equations
  • 1.8 The use of computers
  • 2 The solution of equations
  • 2.1 Introduction
  • 2.2 Location of initial estimates
  • 2.3 Interval halving
  • 2.4 Simple iteration
  • 2.5 Convergence
  • 2.6 Aitken’s extrapolation
  • 2.7 Damped simple iteration
  • 2.8 Newton-Raphson method
  • 2.9 Extended Newton’s method
  • 2.10 Other iterative methods
  • 2.11 Polynomial equations
  • 2.12 Bairstow’s method 56 Worked examples 58 Problems
  • 3 Simultaneous equations
  • 3.1 Introduction
  • 3.2 Elimination methods
  • 3.3 Gaussian elimination
  • 3.4 Extensions to the basic algorithm
  • 3.5 Operation count for the basic algorithm
  • 3.6 Tridiagonal systems
  • 3.7 Extensions to the Thomas algorithm

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