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Taylor & Francis
Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI, Second Edition / Edition 2

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI, Second Edition / Edition 2

by Robert E. White


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Product Details

ISBN-13: 9781482235159
Publisher: Taylor & Francis
Publication date: 11/17/2015
Series: Textbooks in Mathematics Series , #35
Edition description: Revised
Pages: 500
Product dimensions: 6.30(w) x 9.30(h) x 1.20(d)

Table of Contents

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

Steady-State Discrete Models
Steady-State and Triangular Solves
Heat Diffusion and Gauss Elimination
Cooling Fin and Tridiagonal Matrices
Schur Complement
Convergence to Steady-State
Convergence to Continuous Model

Poisson Equation Models
Steady-State and Iterative Methods
Heat Transfer in 2D Fin and SOR
Fluid Flow in a 2D Porous Medium
Ideal Fluid Flow
Deformed Membrane and Steepest Descent
Conjugate Gradient Method

Nonlinear and 3D Models
Nonlinear Problems in One Variable
Nonlinear Heat Transfer in a Wire
Nonlinear Heat Transfer in 2D
Steady-State 3D Heat Diffusion
Time-Dependent 3D Diffusion
High-Performance Computations in 3D

FEM and Fluid Flows
FEM and Linear Shape Functions
FEM with Heat and Fluid Flow
Lax–Wendroff Methods
Shallow Water Wave Model
Navier–Stokes Equations
Discrete Navier–Stokes Equations

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
CPUs and Vector Pipes
Multiprocessor and Multicore Computers
Parallel MATLAB
Parallel MATLAB and SPMD
Introduction to MPI
MPI and Matrix Products

Message Passing Interface
Collective Subroutines
Grouped Datatypes
Fox Algorithm for AB
Shared Memory and OpenMP
Hybrid MPI/OpenMP

Classical Methods for Ax = d
Gauss Elimination
Symmetric Positive Definite Matrices
Domain Decomposition and MPI
SOR and P-Regular Splittings
Parallel ADI Schemes

Krylov Methods for Ax = d
Conjugate Gradient Method
Least Squares
GMRES(m) and MPI

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