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

Author: Guido Buzzi-Ferraris; Flavio Manenti
Publisher: Hoboken : Wiley, 2014.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This fourth in a suite of four 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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Buzzi-Ferraris, Guido.
Differential and Differential-Algebraic Systems for the Chemical Engineer : Solving Numerical Problems.
Hoboken : Wiley, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Guido Buzzi-Ferraris; Flavio Manenti
ISBN: 9783527667130 352766713X
OCLC Number: 890529959
Notes: 3.9 Problem with Discontinuities.
Description: 1 online resource (305 pages)
Contents: Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems; Contents; Preface; 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; 1.5.1 Newton-Cotes Formulae; 1.5.2 Gauss Formulae; 1.6 Algorithms Derived from the Trapezoid Method; 1.6.1 Extended Newton-Cotes Formulae; 1.6.2 Error in the Extended Formulae; 1.6.3 Extrapolation of the Extended Formulae; 1.7 Error Control; 1.8 Improper Integrals; 1.9 Gauss-Kronrod Algorithms. 1.10 Adaptive Methods1.10.1 Method Derived from the Gauss-Kronrod Algorithm; 1.10.2 Method Derived from the Extended Trapezoid Algorithm; 1.10.3 Method Derived from the Gauss-Lobatto Algorithm; 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; 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 Step2.8 Runge-Kutta Methods; 2.9 Explicit Runge-Kutta Methods; 2.9.1 Strategy to Automatically Control the Integration Step; 2.9.2 Estimation of the Local Error; 2.9.2.1 Runge-Kutta-Merson Algorithm; 2.9.2.2 Richardson Extrapolation; 2.9.2.3 Embedded Algorithms; 2.10 Classes Based on Runge-Kutta Algorithms in the BzzMath Library; 2.11 Semi-Implicit Runge-Kutta Methods; 2.12 Implicit and Diagonally Implicit Runge-Kutta Methods; 2.13 Multistep Algorithms; 2.13.1 Adams-Bashforth Algorithms; 2.13.2 Adams-Moulton Algorithms; 2.14 Multivalue Algorithms. 2.14.1 Control of the Local Error2.14.2 Change the Integration Step; 2.14.3 Changing the Method Order; 2.14.4 Strategy for Step and Order Selection; 2.14.5 Initializing a Multivalue Method; 2.14.6 Selecting the First Integration Step; 2.14.7 Selecting the Multivalue Algorithms; 2.14.7.1 Adams-Moulton Algorithms; 2.14.7.2 Gear Algorithms; 2.14.8 Nonlinear System Solution; 2.15 Multivalue Algorithms for Nonstiff Problems; 2.16 Multivalue Algorithms for Stiff Problems; 2.16.1 Robustness in Stiff Problems; 2.16.1.1 Eigenvalues with a Very Large Imaginary Part. 2.16.1.2 Problems with Hard Discontinuities2.16.1.3 Variable Constraints; 2.16.2 Efficiency in Stiff Problems; 2.16.2.1 When to Factorize the Matrix G; 2.16.2.2 How to Factorize the Matrix G; 2.16.2.3 When to Update the Jacobian J; 2.16.2.4 How to Update the Jacobian J; 2.17 Multivalue Classes in BzzMath Library; 2.18 Extrapolation Methods; 2.19 Some Caveats; 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 Reaction; 3.8 Fluidized Bed.

Abstract:

This fourth in a suite of four 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 autho.

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