Numerical methods for engineers and scientists. (2018)

• Record Type: Book
• Further Information: Note: Joe D. Hoffman, Steven Frankel.
• Authors: Hoffman, Joe D, 1934-; Frankel, Steven H (Steven Howard)
• Contents: 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 Polynomial; ; BASIC TOOLS OF NUMERICAL ANALYSIS; . Systems of Linear Algebraic Equations; . Eigenproblems; . Nonlinear Equations; . Polynomial Approximation and Interpolation; . Numerical Differentiation and Difference Formulas; . Numerical Integration; ; Systems 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 Problems; Eigenproblems; . Introduction; . Mathematical Characteristics of Eigenproblems; . The Power Method; . The Direct Method; . The QR Method; . Eigenvectors; . Other Methods; . Programs Summary; . Exercise Problems; Nonlinear 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 Problems; Polynomial 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 Problems; Numerical Differentiation and Difference Formulas; . Introduction; . Unequally Spaced Data; . Equally Spaced Data; . Taylor Series Approach; . Difference Formulas; . Error Estimation and Extrapolation; . Programs; . Summary; . Exercise Problems; Numerical Integration; . Introduction; . Direct Fit Polynomials; . Newton-Cotes Formulas; . Extrapolation and Romberg Integration; . Adaptive Integration; . Gaussian Quadrature; . Multiple Integrals; . Programs; . Summary; . Exercise Problems; ; ORDINARY 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; . Summary; ; One-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 Problems; One-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 Problems; ; PARTIAL 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; . Summary; ; Elliptic 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 Problems; Parabolic 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 Problems; Hyperbolic 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 Problems; The 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 Problems; ; References; Answers to Selected Problems; Index
• Edition: Second edition
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 518; Numerical analysis
• Languages: English
• ISBNs: 9781351990943
• Related ISBNs: 9781482270600; 9781351993845; 9781315274508
• Notes: Note: Description based on CIP data; resource not viewed.
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