LEADER 05369nam 2200625 450 001 9910830222203321 005 20170821201343.0 010 $a3-527-66712-1 010 $a3-527-66710-5 010 $a3-527-66713-X 035 $a(CKB)3710000000230691 035 $a(EBL)1779320 035 $a(SSID)ssj0001375203 035 $a(PQKBManifestationID)11754030 035 $a(PQKBTitleCode)TC0001375203 035 $a(PQKBWorkID)11335691 035 $a(PQKB)10139201 035 $a(MiAaPQ)EBC1779320 035 $a(PPN)188128301 035 $a(EXLCZ)993710000000230691 100 $a20140920h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential and differential-algebraic systems for the chemical engineer $esolving numerical problems /$fGuido Buzzi-Ferraris and Flavio Manenti 210 1$aWeinheim an der Bergstrasse, Germany :$cWiley-VCH,$d2014. 210 4$dİ2014 215 $a1 online resource (305 p.) 300 $aDescription based upon print version of record. 311 $a3-527-33275-8 311 $a1-322-11065-4 320 $aIncludes bibliographical references and index. 327 $aDifferential 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 327 $a1.10 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 327 $a2.7 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 327 $a2.14.1 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 327 $a2.16.1.2 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 327 $a3.9 Problem with Discontinuities 330 $aThis 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 606 $aNumerical analysis$xData processing 606 $aEngineering mathematics 615 0$aNumerical analysis$xData processing. 615 0$aEngineering mathematics. 676 $a518.0 700 $aBuzzi-Ferraris$b G$g(Guido),$0888321 702 $aManenti$b Flavio 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830222203321 996 $aDifferential and differential-algebraic systems for the chemical engineer$94021199 997 $aUNINA