Numerical Methods for Engineers and Scientists

ISBN-13: 9780824704438 / Angielski / Twarda / 2001 / 838 str.

Joe D. Hoffman; Hoffman D. Hoffman

Opis

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book " a good, solid instructional text on the basic tools of numerical analysis."

Recenzje

"…a good, solid instructional text on the basic tools of numerical analysis."
-AIAA Journal

Spis treści

Introduction. Objectives and Approach. Organization of the Book. Examples. Programs. Problems. Significant Digits, Precision, Accuracy, Errors, and Number Representation. Software Packages and Libraries. The Taylor Series and the Taylor PolynomialBASIC TOOLS OF NUMERICAL ANALYSIS. Systems of Linear Algebraic Equations. Eigenproblems. Nonlinear Equations. Polynomial Approximation and Interpolation. Numerical Differentiation and Difference Formulas. Numerical IntegrationSystems of Linear Algebraic Equations. Introduction. Properties of Matrices and Determinants. Direct Elimination Methods. LU Factorization. Tridiagonal Systems of Equations. Pitfalls of Elimination Methods. Iterative Methods. Programs. Summary. Exercise ProblemsEigenproblems. Introduction. Mathematical Characteristics of Eigenproblems. The Power Method. The Direct Method. The QR Method. Eigenvectors. Other Methods. Programs Summary. Exercise ProblemsNonlinear Equations. Introduction. General Features of Root Finding. Closed Domain (Bracketing) Methods. Open Domain Methods. Polynomials. Pitfalls of Root Finding Methods and Other Methods of Root Finding. Systems of Nonlinear Equations. Programs. Summary. Exercise ProblemsPolynomial Approximation and Interpolation. Introduction. Properties of Polynomials. Direct Fit Polynomials. Lagrange Polynomials. Divided Difference Tables and Divided Difference Polynomials. Difference Tables and Difference Polynomials. Inverse Interpolation. Multivariate Approximation. Cubic Splines. Least Squares Approximation. Programs. Summary. Exercise ProblemsNumerical Differentiation and Difference Formulas. Introduction. Unequally Spaced Data. Equally Spaced Data. Taylor Series Approach. Difference Formulas. Error Estimation and Extrapolation. Programs. Summary. Exercise ProblemsNumerical Integration. Introduction. Direct Fit Polynomials. Newton-Cotes Formulas. Extrapolation and Romberg Integration. Adaptive Integration. Gaussian Quadrature. Multiple Integrals. Programs. Summary. Exercise ProblemsORDINARY DIFFERENTIAL EQUATIONS. Introduction. General Features of Ordinary Differential Equations. Classification of Ordinary Differential Equations. Classification of Physical Problems. Initial-Value Ordinary Differential Equations. Boundary-Value Ordinary Differential Equations. SummaryOne-Dimensional Initial-Value Ordinary Differential Equations. Introduction. General Features of Initial-Value ODEs. The Taylor Series Method. The Finite Difference Method. The First-Order Euler Methods. Consistency, Order, Stability, and Convergence. Single-Point Methods. Extrapolation methods. Multipoint Methods. Summary of Methods and Results. Nonlinear Implicit Finite Difference Equations. Higher-Order Ordinary Differential Equations. Systems of First-Order Ordinary Differential Equations. Stiff Ordinary Differential Equations. Programs. Summary. Exercise ProblemsOne-Dimensional Boundary-Value Ordinary Differential Equations. Introduction. General Features of Boundary-Value ODEs. The Shooting (Initial-Value) Method. The Equilibrium (Boundary-Value) Method. Derivative (and Other) Boundary Conditions. Higher-Order Equilibrium Methods. The Equilibrium Method for Nonlinear Boundary-Value Problems. The Equilibrium Method on Nonuniform Grids. Eigenproblems. Programs. Summary. Exercise ProblemsPARTIAL DIFFERENTIAL EQUATIONS. Introduction. General Features of Partial Differential Equations. Classification of Partial Differential Equations. Classification of Physical Problems. Elliptic Partial Differential Equations. Parabolic Partial Differential Equations. Hyperbolic Partial Differential Equaitons. The Convection-Diffusion Equation. Initial Values and Boundary Conditions. Well-Posed Problems. SummaryElliptic Partial Differential Equations. Introduction. General Features of Elliptic PDEs. The Finite Difference Method. Finite Difference Solution of the Laplace Equation. Consistency, Order, and Convergence. Iterative Methods of Solution. Derivative Boundary Conditions. Finite Difference Solution of the Poisson Equation. Higher-Order Methods. Nonrectangular Domains. Nonlinear Equations and Three-Dimensional Problems. The Control Volume Method. Programs. Summary. Exercise ProblemsParabolic Partial Differential Equations. Introduction. General Features of Parabolic PDEs. The Finite Difference Method. The Forward-Time Centered-Space (FTCS) Method. Consistency, Order, Stability, and Convergence. The Richardson and DuFort-Frankel Methods. Implicit Methods. Derivative Boundary Conditions. Nonlinear Equations and Multidimensional Problems. The Convection-Diffusion Equation. Asymptotic Steady State Solution to Propagation Problems. Programs. Summary. Exercise ProblemsHyperbolic Partial Differential Equations. Introduction. General Features of Hyperbolic PDEs. The Finite Difference Method. The Forward-Time Centered-Space (FTCS) Methods and the Lax Method. Lax-Wendroff Type Methods. Upwind Methods. The Backward-Time Centered-Space (BTCS) Method. Nonlinear Equations and Multidimensional Problems. The Wave Equation. Programs. Summary. Exercise ProblemsThe Finite Element Method. Introduction. The Rayleigh-Ritz, Collocation, and Galerkin Methods. The Finite Element Method for Boundary Value Problems. The Finite Element Method for the Laplace (Poisson) Equation. The Finite Element Method for the Diffusion Equation. Programs. Summary. Exercise ProblemsReferencesAnswers to Selected ProblemsIndex

O autorze

Hoffman, Joe D.; Hoffman, Joe D.; Frankel, Steven