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Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems

Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems

Guido Buzzi-Ferraris, Flavio Manenti

ISBN: 978-3-527-33275-5

Jan 2015

302 pages

In Stock

$140.00

Description

Engineers and other applied scientists are frequently faced with models of complex systems for which no rigorous mathematical solution can be calculated. To predict and calculate the behaviour of such systems, numerical approximations are frequently used, either based on measurements of real life systems or on the behaviour of simpler models. This is essential work for example for the process engineer implementing simulation, control and optimization of chemical processes for design and operational purposes.

This fourth in a suite of five practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them.

The volume focuses on differential and differential-algebraic systems, providing numerous real-life industrial case studies to illustrate this complex topic. It describes the methods, innovative techniques and strategies that are all implemented in a freely available toolbox called BzzMath, which is developed and maintained by the authors and provides up-to-date software tools for all the methods described in the book. Numerous examples, sample codes, programs and applications are taken from a wide range of scientific and engineering fields, such as chemical engineering, electrical engineering, physics, medicine, and environmental science. As a result, engineers and scientists learn how to optimize processes even before entering the laboratory.

With additional online material including the latest version of BzzMath Library, installation tutorial, all examples and sample codes used in the book and a host of further examples.

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Preface

DEFINITE INTEGRALS
Introduction
Calculation of Weights
Accuracy of Numerical Methods
Modification of the Integration Inverval
Main Integration Methods
Algorithms Derived from the Trapezoid Method
Error Control
Improper Integrals
Gauss-Kronrod Algorithms
Adaptive Methods
Parallel Computations
Classes for Definite Integrals
Case Study: Optimal Adiabatic Bed Reactors for Sulfur Dioxide with Cold Shot Cooling

ORDINARY DIFFERENTIAL EQUATIONS SYSTEMS
Introduction
Algorithm Accuracy
Equation and System Conditioning
Algorithm Stability
Stiff Systems
Multistep and Multivalue Algorithms for Stiff Systems
Control of the Integration Step
Runge-Kutta Methods
Explicit Runge-Kutta Methods
Classes Based on Runge-Kutta Algorithms in the BzzMath Library
Semi-Implicit Runge-Kutta Methods
Implicit and Diagonally Implicit Runge-Kutta Methods
Multistep Algorithms
Multivalue Algorithms
Multivalue Algorithms for Nonstiff Problems
Multivalue Algorithms for Stiff Problems
Multivalue Classes in BzzMath Library
Extrapolation Methods
Some Caveats

ODE: CASE STUDIES
Introduction
Nonstiff Problems
Volterra System
Simulation of Catalytic Effects
Ozone Decomposition
Robertson's Kinetic
Belousov's Reaction
Fluidized Bed
Problem with Discontinuities
Constrained Problem
Hires Problem
Van der Pol Oscillator
Regression Problems with an ODE Model
Zero-Crossing Problem
Optimization-Crossing Problem
Sparse Systems
Use of ODE Systems to Find Steady-State Conditions of Chemical Processes
Industrial Case: Spectrokinetic Modeling

DIFFERENTIAL AND ALGEBRAIC EQUATION SYSTEMS
Introduction
Multivalue Method
DAE Classes in the BzzMath Library

DAE: CASE STUDIES
Introduction
Van der Pol Oscillator
Regression Problems with the DAE Model
Sparse Structured Matrices
Industrial Case: Distillation Unit

BOUNDARY VALUE PROBLEMS
Introduction
Shooting Methods
Special Boundary Value Problems
More General BVP Methods
Selection of the Approximitating Function
Which and How Many Support Points Have to Be Considered?
Which Variables Should Be Selected as Adaptive Parameters?
The BVP Solution Classes in the BzzMath Library
Adaptive Mesh Selection
Case Studies

APPENDIX
Linking the BzzMath Library to Matlab
Copyrights

Index