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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Examples from this chapter can be found in the directory Vol4_Chapter1 in the WileyVol4.zip file available at the following web site:
http://www.chem.polimi.it/homes/gbuzzi.
1.1 Introduction
This chapter deals with the numerical integration of a function:
(1.1)
In the first part of the chapter, we suppose that the function
leads to no numerical issues within the selected interval
and that
and
can be represented as floating points without any overflow and underflow problems.
We consider the algorithms that approximate the integral
as follows:
(1.2)
These algorithms are different for the position
, where the function is to be evaluated, as well as for the weights
. In the following, we will assume we have all the points distinctly and sequentially placed:
(1.3)
The values of the function
evaluated at the points
shall be denoted as
and the distance between
and
as
. Moreover, if the points are evenly spaced, their distance is denoted by the generic
.
If
and
, the rule is close; if only an external point corresponds to an extreme of the integration interval, the rule is semiopen; if neither of the external points coincide with the integration interv...
Table of contents
Cover
Related Titles
Title Page
Copyright
Preface
Chapter 1: Definite Integrals
Chapter 2: Ordinary Differential Equations Systems
Chapter 3: ODE: Case Studies
Chapter 4: Differential and Algebraic Equation Systems
Chapter 5: DAE: Case Studies
Chapter 6: Boundary Value Problems
Appendix A: Linking the BzzMath Library to Matlab
Appendix B: Copyrights
References
Index
End User License Agreement
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Yes, you can access Differential and Differential-Algebraic Systems for the Chemical Engineer by Guido Buzzi-Ferraris,Flavio Manenti in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Chemical & Biochemical Engineering. We have over one million books available in our catalogue for you to explore.
