Free Download Engineering | Science | Technology Books

File : pdf, 7.9 MB, 255 pages

TOC

Chapter 1 Initial-Value Problems for Ordinary Differential Equations 1
Introduction
Background
Explicit Methods
Stability
Runge-Kutta Methods
Implicit Methods
Extrapolation
Multistep Methods
High-Order Methods Based on Knowledge of allay Stiffness
Systems of Differential Equations
Step-Size Strategies
Mathematical Software

Chapter 2 Boundary-Value Problems for Ordinary Differential Equations: Discrete Variable Methods
Introduction
Background
Initial-Value Methods
Shooting Methods
Multiple Shooting
Superposition
Finite Difference Methods
Linear Second-Order Equations
Flux Boundary Conditions
Integration Method
Nonlinear Second-Order Equations
First-Order Systems
Higher-Order Methods
Mathematical Software

Chapter 3 Boundary-Value Problems for Ordinary Differential Equations: finite Element Methods
Introduction
Background
Piecewise Polynomial Functions
The Galerkin Method
Nonlinear Equations
Inhomogeneous Dirichlet and Flux Boundary Conditions
Mathematical Software
Collocation
Mathematical Software

Chapter 4 Parabolic Partial Differential Equations in One Space Variable
Introduction
Classification of Partial Differential Equations
Method of Lines
finite Differences
Low-Order Time Approximations
The Theta Method
Boundary and Initial Conditions
Nonlinear Equations
Inhomogeneous Media
High-Order Time Approximations
Finite Elements
Galerkin
Collocation
Mathematical Software

Chapter 5 Partial Differential Equations in Two Space Variables
Introduction
Elliptic PDEs-Finite Differences
Background
Laplace’s Equation in a Square
Dirichlet Problem
Neumann Problem
Robin Problem
Variable Coefficients and Nonlinear Problems
Nonuniform Grids
Irregular Boundaries
Dirichlet Condition
Normal Derivative Conditions
Elliptic PDEs-finite Elements
Background
Collocation
Gakrn
Parabolic PDEs in Two Space Variables
Method of Lines
Alternating Direction Implicit Methods
Mathematical Software
Parabolics
Elliptics

Please read the license notice from original resource

Download : pdf1