Introduction to Numerical ComputationAnalysis and Matlab illustrations
Introduction to Numerical ComputationAnalysis and Matlab illustrations
Introduction to Numerical ComputationAnalysis and Matlab illustrations
This ebook contains the following
topics: Mathematical Models and Numerical Approximations, Numerical Computation,
References, Sources of Error, Basic Concepts, Error Propagation, Number
Representation, Rounding Errors in Floating Point, Arithmetic Operations in
Floating Point, Accumulated Errors, IEEE Standard, Introduction, Remainder Term
Estimates, Standard Functions, Range Reduction, Trigonometric Functions,
Introduction, Crude Localization, Iteration Methods, Convergence Analysis, Error
Estimation and StoppingCriteria, Algebraic Equations, Square Root, Nonlinear
Systems, Introduction, Interpolation by Polynomials, Linear Interpolation,
Lagrange Interpolation, Hermite Interpolation, Splines, Linear Spline Functions,
Cubic Splines, Introduction, Richardson Extrapolation, Introduction, Trapezoidal
Rule, Adaptive Quadrature, Introduction, Triangular Systems, Gaussian
Elimination, Pivoting, LU Factorization, Band Matrices, Inverse Matrix, Vector
and Matrix Norms, Sensitivity Analysis, Rounding Errors, Estimation of Condition
Number, Overdetermined Systems, QR Factorization, Introduction, Important
Concepts, Least Squares Method, Orthogonal Functions, Orthogonal Polynomials,
Legendre Polynomials, Chebyshev Polynomials, Discrete Cosine Transform, Minimax
Approximation, Introduction, Initial Value Problems, Local and Global Error, An
Implicit Method, Stability, Adaptive Step Length Control, Boundary Value
Problems, A Finite Element Method, The Shooting Method, Mathematical Models and
Numerical Approximations
Author(s): Lars Elden
Linde Wittmeyer-Koch Hans Bruun Nielsen
Numerical Topics in Fluid
Dynamics Computation!!! Peter Bastian Authored - This PDF covers advanced
numerical computation topics but puts more emphasis on the solution of
computational fluid dynamics. The book starts with the modeling of immiscible
fluid flow in a composite porous medium, thus laying down the basics for the
equations of multiphase fluid flow. It then provides fully implicit methods that
have been used to find the finite volume discretization of systems for complex
algebraic equations. Two important chapters are the parallelization methods that
result in higher productivity of computation and the UG framework used for
carrying out grid computations. Numerical results are then presented, which
allow deriving some conclusions concerning practical applications and
performance. The document will be particularly useful to researchers and
engineers studying computational fluid dynamics and related numerical modeling
problems.
This
note introduces elementary programming concepts including variable types, data
structures, and flow control. After an introduction to linear algebra and
probability, it covers numerical methods relevant to mechanical engineering,
including approximation, integration, solution of linear and nonlinear equations, ordinary
differential equations, and deterministic and probabilistic approaches.
Author(s): Prof.
Anthony T. Patera, Prof. Daniel Frey and Prof. Nicholas Hadjiconstantinou
The
resource described here is an overview of numerical methods important in the
study of computational science and engineering. The text starts off with
Computing with Matrices and Vectors, foundational elements in many algorithms.
The note moves forward and explains Direct Methods for Linear Systems of
Equations and Direct Methods for Linear Least Squares Problems, important
problem-solving aspects in linear algebra. The Filtering Algorithms for data
processing are reviewed, while Data Interpolation and Data Fitting in 1D discuss
ways of approximating onedimensional data. Approximation of Functions in 1D and
Numerical Quadrature introduce the techniques on function approximation and
integration. It also discusses Iterative Methods for Non-Linear Systems of
Equations and Eigenvalues-a critical topic needed for solving complex systems.
It finally includes Numerical Integration and Structure Preserving Integration,
fundamental to perform numerical calculations with appropriate accuracy in
scientific computing.
It gives an explanation
of all the different numerical methods of scientific computing. It starts with
the basics, which is Root Finding and Orthogonal Functions, solving equations
and analyzing functions. Finite Differences and Divided Differences included for
the needs in the process of numerical differentiation and interpolation.
Interpolation and Curve Fitting are given to outline estimation and modeling. It
also includes Z-Transforms and Summation Formulas for signal processing and
numerical summation. Quadrature Formulas and Ordinary Differential Equations are
explained for integration and the solution of differential equations. Partial
Differential Equations, Integral Equations, and Stability and Error Analysis
form the advanced topics for numerical methods coverage. Further, Monte Carlo
Techniques, Message Passing Interface, and Simulation Modeling are included to
point out methods for probabilistic simulations and parallel computing.