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

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.

Table of Contents:
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

About the Author :
Guido Buzzi-Ferraris is full professor of process systems engineering at Politecnico die Milano, Italy, where he holds two courses: "Methods and Numerical Applications in Chemical Engineering" and "Regression Models and Statistics". He works on numerical analysis, statistics, differential systems, and optimization. He has authored books of international relevance on numerical analysis, such as "Scientific C++" edited by Addison-Wesley, and over than 200 papers on international magazines. He is the inventor and the developer of BzzMath library, which is currently adopted by academies, R&D groups, and industries. He is permanent member of the "EFCE Working Party - Computer Aided Process Engineering" since 1969 and editorial advisory board of "Computers & Chemical Engineering" since 1987. Flavio Manenti is assistant professor of process systems engineering at Politecnico di Milano, Italy. He obtained his academic degree and PhD at Politecnico di Milano, where he currently collaborates with Professor Buzzi-Ferraris. He holds courses on "Process Dynamics and Control of Industrial Processes" and "Supply Chain Optimization" and he works on numerical analysis, process control and optimization. He has also received international scientific awards, such as Memorial Burianec (Prague, CZ) and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.