This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch,
and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to
numerical computation. The text begins with the basics like error analysis and
computer arithmetic, which gives a very solid ground for the origin and handling
of numerical errors. It proceeds further to explain more basic topics related to
function evaluation, solutions of nonlinear equations, and interpolation
techniques. Next, it describes procedures for improving numerical estimates
using differentiation and Richardson extrapolation. This is followed by full
details of integration, systems of linear equations, and approximation. Finally,
ordinary differential equations complete a thorough course of study that will
prepare the reader with both the theory and practice that will serve in carrying
out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans
Bruun Nielsen
This is an exhaustive PDF written by Lars Elden, Linde Wittmeyer-Koch,
and Hans Bruun Nielsen. In fact, this really is an exemplary introduction to
numerical computation. The text begins with the basics like error analysis and
computer arithmetic, which gives a very solid ground for the origin and handling
of numerical errors. It proceeds further to explain more basic topics related to
function evaluation, solutions of nonlinear equations, and interpolation
techniques. Next, it describes procedures for improving numerical estimates
using differentiation and Richardson extrapolation. This is followed by full
details of integration, systems of linear equations, and approximation. Finally,
ordinary differential equations complete a thorough course of study that will
prepare the reader with both the theory and practice that will serve in carrying
out numerical computations.
Author(s): Lars Elden, Linde Wittmeyer-Koch, Hans
Bruun Nielsen
This
PDF is prepared by Gonzalo Galiano Casas and Esperanza Garcia Gonzalo from the
Department of Mathematics at Oviedo University. With a view to keeping things
compact, this document initiates with finite arithmetic and error analysis,
which forms the basis necessary for understanding the issue of numerical
precision and limitations. It considers methods for nonlinear equations,
interpolation, and approximation. Key sections on numerical differentiation and
integration give hands-on tools both for data analysis and the solution of
mathematical problems. It also covers systems of linear equations and
optimization, rounding it out for students and practitioners who might want to
apply the numerical methods through a variety of problems.
Author(s): Gonzalo Galiano Casas, Esperanza Garcia Gonzalo, Dept. of Mathematics, Oviedo University
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.
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.