## Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI

Published:
Author(s):

Hardback
\$125.95
ISBN 9781584883647
Cat# C3642
eBook
ISBN 9780203494479
Cat# TFE1009

### Features

• Introduces the concepts and techniques at the core of computational science
• Takes a learn-by-doing approach, providing a wealth of MATLAB, Fortran, and C++ code both within the book and at www4.ncsu.edu/~white
• Presents many of the most current numerical methods including the Schur complement, domain decomposition, and conjugate gradient methods
• Explores a range of applications, from heat diffusion and fluid flow to epidemics, option contracts, and image restoration
• ### Summary

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white.

This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether used as an undergraduate textbook, for self-study, or for reference, it builds the foundation you need to make numerical modeling and simulation integral parts of your investigational toolbox.

INTRODUCTION
DISCRETE TIME-SPACE MODELS
Newton Cooling Models
Heat Diffusion in a Wire
Diffusion in a Wire with Little Insulation
Flow and Decay of a Pollutant in a Stream
Heat and Mass Transfer in Two Directions
Convergence Analysis

Heat Diffusion and Gauss Elimination
Cooling Fin and Tridiagonal Matrices
Schur Complement
Convergence to Continuous Model

POISSON EQUATION MODELS
Heat Transfer in 2D Fin and SOR
Fluid Flow in a 2D Porous Medium
Ideal Fluid Flow
Deformed Membrane and Steepest Descent

NONLINEAR AND 3D MODELS
Nonlinear Problems in One Variable
Nonlinear Heat Transfer in a Wire
Nonlinear Heat Transfer in 2D
Time Dependent 3D Diffusion
High Performance Computations in 3D

EPIDEMICS, IMAGES AND MONEY
Epidemics and Dispersion
Epidemic Dispersion in 2D
Image Restoration
Restoration in 2D
Option Contract Models
Black-Scholes Model for Two Assets

HIGH PERFORMANCE COMPUTING
Vector Computers and Matrix Products
Vector Computations for Heat Diffusion
Multiprocessors and Mass Transfer
MPI and IBM/SP
MPI and Matrix Products
MPI and 2D Models

MESSAGE PASSING INTERFACE
Basic MPI Subroutines
Gather and Scatter
Grouped Data Types
Communicators
Fox Algorithm for AB

CLASSICAL METHODS FOR Ax = D
Gauss Elimination
Symmetric Positive Definite Matrices
Domain Decomposition and MPI
SOR and P-Regular Splittings
SOR and MPI

KRYLOV METHODS FOR Ax = D
Preconditioners
PCG and MPI
Least Squares
GMRES
GMRES(m) and MPI
BIBLIOGRAPHY
INDEX

### Editorial Reviews

"Overall this book is not just about mathematics, not just about computing, and not just about applications, but about computational science. One interesting characteristic of this book is the writing style…another interesting thing found in this book is an abundance of MATLAB® code…this book is suitable for an undergraduate level topics course."
-Zentralblatt MATH