Numerical Methods for 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.
Author(s): John Henry Heinbockel
NA Pages 
Numerical Computation by Peter Bastian
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.
Author(s): Peter Bastian
236 Pages
Numerical Computation for Mechanical Engineers
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
NA Pages
Numerical Methods for Computational Science and Engineering
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.
Author(s): Prof. R. Hiptmair
839 Pages
Numerical Methods for 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.
Author(s): John Henry Heinbockel
NA Pages
