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

Author: G Buzzi-Ferraris; Flavio Manenti
Publisher: Weinheim, Germany : Wiley-VCH, 2014.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: G Buzzi-Ferraris; Flavio Manenti
ISBN: 9783527667109 3527667105 9783527667130 352766713X 1322110654 9781322110653 9783527332755 3527332758 9783527667123 3527667121 9783527667116 3527667113
OCLC Number: 890441787
Description: 1 online resource
Contents: Related Titles; Title Page; Copyright; Preface; Outline of This Book; Notation; BzzMath Library Style; Basic Requirements for Using BzzMath Library; How to Install Examples Collected in This Book; A Few Steps to Install BzzMath Library; Include the BzzMath Library in a Calculation Program; Chapter 1: Definite Integrals; 1.1 Introduction; 1.2 Calculation of Weights; 1.3 Accuracy of Numerical Methods; 1.4 Modification of the Integration Interval; 1.5 Main Integration Methods; 1.6 Algorithms Derived from the Trapezoid Method; 1.7 Error Control; 1.8 Improper Integrals. 1.9 Gauss-Kronrod Algorithms1.10 Adaptive Methods; 1.11 Parallel Computations; 1.12 Classes for Definite Integrals; 1.13 Case Study: Optimal Adiabatic Bed Reactors for Sulfur Dioxide with Cold Shot Cooling; Chapter 2: Ordinary Differential Equations Systems; 2.1 Introduction; 2.2 Algorithm Accuracy; 2.3 Equation and System Conditioning; 2.4 Algorithm Stability; 2.5 Stiff Systems; 2.6 Multistep and Multivalue Algorithms for Stiff Systems; 2.7 Control of the Integration Step; 2.8 Runge-Kutta Methods; 2.9 Explicit Runge-Kutta Methods. 2.10 Classes Based on Runge-Kutta Algorithms in the BzzMath Library2.11 Semi-Implicit Runge-Kutta Methods; 2.12 Implicit and Diagonally Implicit Runge-Kutta Methods; 2.13 Multistep Algorithms; 2.14 Multivalue Algorithms; 2.15 Multivalue Algorithms for Nonstiff Problems; 2.16 Multivalue Algorithms for Stiff Problems; 2.17 Multivalue Classes in BzzMath Library; 2.18 Extrapolation Methods; 2.19 Some Caveats; Chapter 3: ODE: Case Studies; 3.1 Introduction; 3.2 Nonstiff Problems; 3.3 Volterra System; 3.4 Simulation of Catalytic Effects; 3.5 Ozone Decomposition; 3.6 Robertson's Kinetic. 3.7 Belousov's Reaction3.8 Fluidized Bed; 3.9 Problem with Discontinuities; 3.10 Constrained Problem; 3.11 Hires Problem; 3.12 Van der Pol Oscillator; 3.13 Regression Problems with an ODE Model; 3.14 Zero-Crossing Problem; 3.15 Optimization-Crossing Problem; 3.16 Sparse Systems; 3.17 Use of ODE Systems to Find Steady-State Conditions of Chemical Processes; 3.18 Industrial Case: Spectrokinetic Modeling; Chapter 4: Differential and Algebraic Equation Systems; 4.1 Introduction; 4.2 Multivalue Method; 4.3 DAE Classes in the BzzMath Library; Chapter 5: DAE: Case Studies; 5.1 Introduction. 5.2 Van der Pol Oscillator5.3 Regression Problems with the DAE Model; 5.4 Sparse Structured Matrices; 5.5 Industrial Case: Distillation Unit; Notations for Table 5.1; Chapter 6: Boundary Value Problems; 6.1 Introduction; 6.2 Shooting Methods; 6.3 Special Boundary Value Problems; 6.4 More General BVP Methods; 6.5 Selection of the Approximating Function; 6.6 Which and How Many Support Points Have to Be Considered?; 6.7 Which Variables Should Be Selected as Adaptive Parameters?; 6.8 The BVP Solution Classes in the BzzMath Library; 6.9 Adaptive Mesh Selection; 6.10 Case studies.
Responsibility: Guido Buzzi-Ferraris, Flavio Manenti.

Abstract:

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  Read more...

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