@article{HungenbergSchwedeWulkowetal.2021, author = {Hungenberg, Klaus-Dieter and Schwede, Christian and Wulkow, Michael and Wulkow, Niklas}, title = {Determination of reactivity ratios for acrylic acid and its dimer from classical parameter estimation and Bayesian approach}, journal = {Canadian Journal of Chemical Engineering}, doi = {https://doi.org/10.1002/cjce.24330}, pages = {1 -- 10}, year = {2021}, abstract = {The reactivity ratios of acrylic acid (AA, M1) and its dimer beta-acroyloxypropionic acid (diAA, M2) are determined from cumulative copolymerization data by two different methods: classical parameter estimation (PE) by minimizing the objective function and a Bayesian analysis. Classical PE gives r1 =0.74 and r2 = 1.23 at the minimum of the residual. From the Bayesian analysis, the probability distribution of the parameter sets is obtained, revealing the existence of parameter sets with rather the same probability. The influence of the number of data and the size of the measurement error are discussed.}, language = {en} } @article{WulkowTelgmannHungenbergetal.2021, author = {Wulkow, Niklas and Telgmann, Regina and Hungenberg, Klaus-Dieter and Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples}, volume = {30}, journal = {Macromolecular Theory and Simulations}, doi = {10.1002/mats.202100017}, year = {2021}, abstract = {Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.}, language = {en} } @misc{DeuflhardHuisingaJahnkeetal.2007, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9471}, number = {07-04}, year = {2007}, abstract = {\begin{abstract} In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signalling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equat ion, also known as the chemical master equation (CME). Up to now, the CME has almost exclusively been treated by Monte-Carlo techniques, the most prominent of which is the simulation algorithm suggest ed by Gillespie in 1976. Since this algorithm requires an update for each single reaction event, realizations can be computationally very costly. As an alternative, we here propose a novel approach, which focuses on the discrete partial differential equation (PDE) structure of the CME and thus allows to adopt ideas from adaptive discrete Galerkin methods (as designed by two of the present authors in 1989), which have proven to be highly efficient in the mathematical modelling of polyreaction kinetics. Among the two different options of discretizing the CME as a discrete PDE, the method of lines approach (first space, then time) and the Rothe method (first time, then space), we select the latter one for clear theoretical and algorithmic reasons. First numeric al experiments at a challenging model problem illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further research. \end{abstract}}, language = {en} } @article{HornWulkow2005, author = {Horn, H. and Wulkow, Michael}, title = {Simulation von Wachstum und Abtrag der Biomasse - Eine exemplarische Betrachtung f{\"u}r eine 2D-Modellierung}, volume = {77}, journal = {Chem. Ing. Technik}, number = {4}, pages = {418 -- 424}, year = {2005}, language = {en} } @article{HornWulkow1996, author = {Horn, H. and Wulkow, Michael}, title = {Modellierung von Einleitungen in kleine Fließgew{\"a}sser}, volume = {137}, journal = {gwf Wasser Abwasser}, year = {1996}, language = {en} } @article{HuisingaTelgmannWulkow2006, author = {Huisinga, Wilhelm and Telgmann, R. and Wulkow, Michael}, title = {The virtual lab approach to pharmacokinetic}, volume = {11}, journal = {Drug Discov Today}, pages = {800 -- 805}, year = {2006}, language = {en} } @article{HungenbergChenZhangetal.2001, author = {Hungenberg, K.-D. and Chen, C.-C. and Zhang, F. and Wulkow, Michael and Stubbe, G. and Nieken, U.}, title = {Design of Polymer Processes Using the Coupling of Commercial Simulation Packages Polymers Plus and PREDICI}, volume = {137}, journal = {DECHEMA Monographs}, pages = {237 -- 245}, year = {2001}, language = {en} } @article{HungenbergKnollWulkow1997, author = {Hungenberg, K.-D. and Knoll, K. and Wulkow, Michael}, title = {Absolute Propagation Rate Coefficients in Radical Polymerization from Gel Permeation Chromatography of Polymers Produced by Intermittent Initiation}, volume = {6}, journal = {Macromol. Theory Simul.}, year = {1997}, language = {en} } @article{IedemaWulkowHoefsloot2007, author = {Iedema, P. and Wulkow, Michael and Hoefsloot, H.}, title = {Conditional Monte Carlo sampling to find branching architectures of polymers from radical polymerizations with transfer to polymer and recombination termination}, volume = {48}, journal = {Polymer}, number = {6}, pages = {1770 -- 1784}, year = {2007}, language = {en} } @article{IedemaWulkowHoefsloot:2000, author = {Iedema, P. and Wulkow, Michael and Hoefsloot:, H.}, title = {Modeling Molecular Weight and Degree of Branching Distribution of low density Polyethylene}, volume = {33}, journal = {Macromolecules}, pages = {7173 -- 7184}, year = {2000}, language = {en} } @article{KatzerPauerMoritzetal.2012, author = {Katzer, J. and Pauer, W. and Moritz, H.-U. and Wulkow, Michael}, title = {Thermal polymerization of styrene Part B}, volume = {6}, journal = {Macromol. React. Eng}, pages = {225 -- 238}, year = {2012}, language = {en} } @article{LinGrimmWulkowetal.2008, author = {Lin, P.-J. and Grimm, L. and Wulkow, Michael and Hempel, D. and Krull, R.}, title = {Population Balance Modeling of the Conidial Aggregation of Aspergillus niger}, volume = {99}, journal = {Biotechnology and Bioengineering}, number = {2}, pages = {341 -- 350}, year = {2008}, language = {en} } @article{MuellerYanWulkow1997, author = {M{\"u}ller, A. and Yan, D. and Wulkow, Michael}, title = {Molecular Parameters of Hyperbranched Polymers Made by Self-condensing Vinyl Polymerization, 1. Molecular weight distribution}, volume = {30}, journal = {Macromolecules}, pages = {7015}, year = {1997}, language = {en} } @article{OchoaWulkow2012, author = {Ochoa, J.G. and Wulkow, Michael}, title = {DNA damages as a Depolymerization Process}, volume = {23}, journal = {International Journal of Modern Physics C}, number = {03}, pages = {1250018 -- 1}, year = {2012}, language = {en} } @article{ReuterKrauseWulkowetal.2003, author = {Reuter, H. and Krause, G. and Wulkow, Michael and M{\"o}nig, A. and Horn, H.}, title = {A water quality management tool for river basins}, volume = {48}, journal = {Wat. Sci. Techn.}, number = {10}, pages = {47 -- 53}, year = {2003}, language = {en} } @article{ReynhoutMeuldijkDrinkenburgetal.2005, author = {Reynhout, X. and Meuldijk, J. and Drinkenburg, B. and Iedema, P. and Wulkow, Michael}, title = {A Novel Method to Model Emulsion Polymerization Kinetics}, volume = {44}, journal = {Polymer-Plastics Tech. Eng.}, number = {4}, pages = {707 -- 740}, year = {2005}, language = {en} } @article{SchmidtBuschLilgeetal.2005, author = {Schmidt, Christian-Ulrich and Busch, Markus and Lilge, Dieter and Wulkow, Michael}, title = {Detailed Molecular Structure Modeling - A Path Forward to Designing Application Properties of ldPE}, volume = {290}, journal = {Macromolecular Materials and Engineering}, pages = {404}, year = {2005}, language = {en} } @article{SchuetteWulkow2010, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {A hybrid Galerkin-Monte-Carlo approach to higher-dimensional population balances in polymerization kinetics}, volume = {4}, journal = {Macromol. React. Eng.}, pages = {562 -- 577}, year = {2010}, language = {en} } @article{TeichmannLiebeltReuschenbachetal.2001, author = {Teichmann, L. and Liebelt, U. and Reuschenbach, P. and Wulkow, Michael and Horn, H.}, title = {Two dimensional simulation of mass transport and nitrification in the river Rhine}, volume = {1}, journal = {Eng. Life Sci.}, number = {4}, pages = {145 -- 149}, year = {2001}, language = {en} } @article{Wulkow2008, author = {Wulkow, Michael}, title = {Feature article - Computer Aided Modeling of Polymer Reaction Engineering - The Status of Predici, 1 - Simulation}, volume = {2}, journal = {Macromol. React. Eng.}, pages = {461 -- 494}, year = {2008}, language = {en} } @article{Wulkow1996, author = {Wulkow, Michael}, title = {Feature article - The Simulation of Molecular Weight Distributions in Polyreaction Kinetics by Discrete Galerkin Methods}, volume = {5}, journal = {Macromol. Theory Simul.}, pages = {393 -- 416}, year = {1996}, language = {en} } @article{WulkowBuschDavisetal.2004, author = {Wulkow, Michael and Busch, Markus and Davis, Thomas P. and Barner-Kowollik, Christopher}, title = {Implementing the Reversible Addition Fragmentation Chain Transfer (RAFT) Process in Predici.}, volume = {42}, journal = {Journal of Polymer Science}, pages = {1441}, year = {2004}, language = {en} } @article{WulkowGerstlauerNieken2001, author = {Wulkow, Michael and Gerstlauer, A. and Nieken, U.}, title = {Modeling of Crystallization Processes using PARSIVAL}, volume = {56}, journal = {Chem. Eng. Sci.}, pages = {2575 -- 2588}, year = {2001}, language = {en} } @article{NikitinWulkowSchuette2013, author = {Nikitin, B. A. and Wulkow, Michael and Sch{\"u}tte, Christof}, title = {Modeling of Free Radical Styrene/Divinylbenzene Copolymerization with the Numerical Fractionation Technique}, volume = {22}, journal = {Macromolecular Theory and Simulation}, number = {9}, doi = {10.1002/mats.201300125}, pages = {475 -- 489}, year = {2013}, language = {en} } @article{DeuflhardWulkow1989, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational treatment of polyreaction kinetics by orthogonal polynomials of a discrete variable}, volume = {1}, journal = {IMPACT Comput. Sci. Eng.}, number = {3}, pages = {269 -- 301}, year = {1989}, language = {en} } @incollection{DeuflhardWulkow1995, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Simulationsverfahren f{\"u}r die Polymerchemie}, booktitle = {Mathematik in der Praxis. Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin}, editor = {et al. Bachem, Achim}, publisher = {Berlin: Springer-Verlag}, pages = {117 -- 136}, year = {1995}, language = {en} } @incollection{WulkowDeuflhard1992, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions}, booktitle = {Computational Ordinary Differential Equations}, editor = {Fatunla, S.}, publisher = {University Press, Nigeria}, pages = {287 -- 306}, year = {1992}, language = {en} } @article{SchuetteWulkow2010, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {A Hybrid Galerkin-Monte-Carlo Approach to Higher-Dimensional Population Balances in Polymerization Kinetics}, volume = {4}, journal = {Macromol. React. Eng.}, number = {9-10}, doi = {10.1002/mren.200900073}, pages = {562 -- 577}, year = {2010}, language = {en} } @article{DeuflhardHuisingaJahnkeetal.2008, author = {Deuflhard, Peter and Huisinga, Wilhelm and Jahnke, Tobias and Wulkow, Michael}, title = {Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation}, volume = {30}, journal = {SIAM J. Sci. Comput}, number = {6}, pages = {2990 -- 3011}, year = {2008}, language = {en} } @article{SchuetteWulkow1992, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of Raman Spectroscopy.}, journal = {preprint}, year = {1992}, language = {en} } @article{AppelBockhornWulkow1999, author = {Appel, J{\"o}rg and Bockhorn, Henning and Wulkow, Michael}, title = {Numerical Simulation of Soot Particle Size Distributions with a Discrete Galerkin Method}, volume = {2}, journal = {Proceedings of the Workshop Scientific Computing in Chemical Engineering II}, year = {1999}, language = {en} } @article{BockhornHornungHornungetal.1999, author = {Bockhorn, Henning and Hornung, Andreas and Hornung, Ursel and Jakobstr{\"o}er, Petra and Wulkow, Michael}, title = {Modeling of Thermal Degradation of Polymers}, volume = {1}, journal = {Proceedings of the Workshop Scientific Computing in Chemical Engineering II}, year = {1999}, language = {en} } @article{BrueggemannBauerFuchsetal.2008, author = {Br{\"u}ggemann, Stefan and Bauer, Nanette and Fuchs, Eberhard and Polt, Axel and Wagner, Bernhard and Wulkow, Michael}, title = {Support of Strategic Business Decisions at BASF's Largest Integrated Production Site Based on Site-Wide Verbund Simulation}, volume = {25}, journal = {Computer Aided Chem. Eng.}, pages = {925 -- 930}, year = {2008}, language = {en} } @article{BuschMuellerWulkow2003, author = {Busch, Markus and M{\"u}ller, M. and Wulkow, Michael}, title = {The use of Simulation Techniques in Developing Kinetic Models for Polymerizations}, volume = {26}, journal = {Chem. Eng. Technol.}, pages = {1031}, year = {2003}, language = {en} } @article{BuschWulkow2003, author = {Busch, Markus and Wulkow, Michael}, title = {Modellierung differenzierter mikrostruktureller Eigenschaften}, volume = {75}, journal = {Chem. Ing. Tech.}, pages = {1027}, year = {2003}, language = {en} } @article{GroschBriesenWulkowetal.2007, author = {Grosch, R. and Briesen, Heiko and Wulkow, Michael and Marquardt, Wolfgang}, title = {Generalization and numerical investigation of QMOM for crystallization processes}, volume = {53}, journal = {AIChE J.}, pages = {207 -- 227}, year = {2007}, language = {en} } @article{HornNeuWulkow2001, author = {Horn, H. and Neu, T. and Wulkow, Michael}, title = {Modelling the Structure and Function of Extracellular Polymeric Substances in Biofilms with new Numerical Techniques}, volume = {43}, journal = {Wat. Sci. Techn.}, number = {´6}, pages = {121 -- 127}, year = {2001}, language = {en} } @misc{AckermannWulkow1990, author = {Ackermann, J{\"o}rg and Wulkow, Michael}, title = {MACRON - A Program Package for Macromalecular Reaction Kinetics.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-423}, number = {SC-90-14}, year = {1990}, abstract = {This paper presents the new program package MACRON for the simulation of macromolecular kinetics including standard chemical reactions. Such problems lead to countable (possibly) infinite systems of ordinary differential equations (CODE's), which are numerically treated by the so-called discrete Galerkin method here. By a chemical compiler the required analytical preprocessing is performed, such that the complete reaction system, standard kinetics as well as macromolecular reactions, can be entered in the chemical formalism. Typical macromolecular reaction steps are chain addition, termination, chain transfer and degradation (cracking). In order to ensure efficiency and reliability, high sophisticated numerical routines are built within the package. MACRON can be used without a detailed knowledge of the used numerical methods. As an illustration the application of MACRON to some realistic problems is presented.}, language = {en} } @misc{WulkowAckermann1990, author = {Wulkow, Michael and Ackermann, J{\"o}rg}, title = {Numerical Treatment of Polyreactions - Recent Developments.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-439}, number = {SC-90-15}, year = {1990}, abstract = {The mathematical modeling of macromolecular reactions leads to countable (possibly infinite) systems of ordinary differential equations (CODE's). This paper reviews two recent developments of the so-called discrete Galerkin method, which has been developed for the numerical treatment of countable systems, which arise e.g. in polymer chemistry. The first approach can be considered as a method of lines with moving basis functions and has been implemented recently in the program package MACRON. The second type of the Galerkin method is characterized by a so-called outer time discretization of the complete problem and an appropriate and efficient solution of the arising subproblems. This method is realized in the research code CODEX.}, language = {en} } @misc{DeuflhardWulkow1994, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Simulationsverfahren f{\"u}r die Polymerchemie}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1502}, number = {SC-94-22}, year = {1994}, abstract = {Die enorme algorithmische Beschleunigung durch diskrete Galerkin-Methoden f{{\"u}}r abz{{\"a}}hlbare Differentialgleichungssysteme hat der Simulation von Polymerisationsprozessen neue, industriell relevante Problembereiche er{{\"o}}ffnet, die mit den bis dahin verf{{\"u}}gbaren Methoden nicht zug{{\"a}}nglich waren.}, language = {de} } @misc{Wulkow1991, author = {Wulkow, Michael}, title = {Adaptive Treatment of Polyreactions in Weighted Sequence Spaces.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-673}, number = {SC-91-17}, year = {1991}, abstract = {Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and statistics. They can be considered as ordinary differential equations in sequence spaces. In this work, a fully adaptive algorithm for the computational treatment of such systems is developed. The method is based on a time discretization of an abstract Cauchy problem in Hilbert space and a discrete Galerkin approach for the discretization of the arising stationary subproblems. The Galerkin method uses orthogonal functions of a discrete variable, which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations are solved adaptively either by use of analytical properties of the orthogonal functions or by an appropriate numerical summation. The resulting algorithm CODEX is applied to examples of technological interest, in particular from polymer chemistry.}, language = {en} } @misc{AckermannWulkow1991, author = {Ackermann, J{\"o}rg and Wulkow, Michael}, title = {The Treatment of Macromolecular Processes with Chain-Length-Dependent Reaction Coefficients - An Examplefrom Soot Formation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-682}, number = {SC-91-18}, year = {1991}, abstract = {The description of chain length distributions in macromolecular reaction kinetics leads to so-called countable systems of differential equations. In particular, when the appearing reaction rate coefficients depend on the chain length of the reacting macromolecules itself, an efficient numerical treatment of these systems is very difficult. Then even the evaluation of the right-hand side of the system can become prohibitively expensive with respect to computing time. In this paper we show how the discrete Galerkin method can be applied to such problems. The existing algorithm CODEX is improved by use of a multiplicative error correction scheme for time discretization and a new type of numerical preprocessing by means of a Gauss summation. Both ideas are exemplary for a wide class of approximation types and are described very briefly here. The new numerical techniques are tested on an example from soot formation, where the coagulation of molecules is modeled in terms of reaction coefficients depending on the surface of the particles and their collision frequency.}, language = {en} } @misc{DeuflhardWulkow1988, author = {Deuflhard, Peter and Wulkow, Michael}, title = {Computational Treatment of Polyreaction Kinetics by Orthogonal Polynomials of a Discrete Variable.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-140}, number = {SC-88-06}, year = {1988}, abstract = {The paper presents a new approach to the computational treatment of polyreaction kinetics. This approach is characterized by a Galerkin method based on orthogonal polynomials of a discrete variable, the polymer degree (or chain length). In comparison with the known competing approaches (statistical moment treatment, Galerkin methods for continuous polymer models), the suggested method is shown to avoid the disadvantages and preserve the adventages of either of them. The basic idea of the method is the construction of a discrete inner product associated with a reasonably chosen probability density function. For the so-called Schulz-Flory distribution one thus obtains the discrete Laguerre polynomials, whereas the Poisson distribution leads to the Charlier polynomials. Numerical experiments for selected polyreaction mechanisms illustrate the efficiency of the proposed method.}, language = {en} } @misc{SchuetteWulkow1992, author = {Sch{\"u}tte, Christof and Wulkow, Michael}, title = {Quantum Theory with Discrete Spectra and Countable Systems of Differential Equations - A Numerical Treatment of RamanSpectroscopy.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-778}, number = {SC-92-07}, year = {1992}, abstract = {Models for occupation dynamics in discrete quantum systems lead to large or even infinite systems of ordinary differential equations. Some new mathematical techniques, developed for the simulation of chemical processes, make a numerical solution of countable systems of ordinary differential equations possible. Both, a basic physical concept for the construction of such systems and the structure of the numerical tools for solving them are presented. These conceptual aspects are illustrated by a simulation of an occupation process from spectroscopy. In this example the structures of rotation spectra observed in infrared spectroscopy are explained and some possibilities for an extension of the model are shown.}, language = {en} } @misc{BuddeWulkow1989, author = {Budde, Uwe and Wulkow, Michael}, title = {Computation of Molecular Weight Distributions for Free Radical Polymerization Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-253}, number = {SC-89-07}, year = {1989}, abstract = {Modeling of free radical polymerization leads to very large and usually stiff systems of ordinary differential equations which cannot be solved directly in an efficient way. This paper presents the application of a new approach called discrete Galerkin method to a realistic example - the polymerization of methyl methacrylate(MMA). The method is characterized by a Galerkin approximation on the basis of orthogonal polynomials of a discrete variable which represents the polymer degree. It allows the efficient computation of solutions of complete kinetic schemes with time- or moment-dependent reaction coefficients by reducing the complexity to a few differential equations. The approximation error can be controlled by an error estimation. In the case of MMA polymerization a reduction of computational effort by a factor of about 25 compared to a standard method can be obtained for the quasi-steady-state approximation of the model. In addition solutions of the instationary kinetic scheme can be easily computed.}, language = {en} } @misc{WulkowDeuflhard1990, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-292}, number = {SC-90-01}, year = {1990}, abstract = {The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.}, language = {en} } @misc{DeuflhardNowakWulkow1990, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-359}, number = {SC-90-07}, year = {1990}, abstract = {The paper surveys three aspects of chemical computing, which seem to play a role in recent developments. First, extrapolation methods for the numerical treatment of differential- algebraic equations are introduced. The associated extrapolation code LIMEX has reached a certain level of sophistication, which makes it a real competitor to the elsewhere widely used multi-step code DASSL of Petzold. Second, adaptive methods of lines for partial differential equations such as those arising in combustion problems are treated. Both static and dynamic regridding techniques are discussed in some detail. Finally, some new ideas about the treatment of the kinetic equations arising from polymer reactions are presented. The new feature of the suggested approach is the application of a Galerkin procedure using sets of orthogonal polynomials over a discrete variable (which, of course, in the case of polymer reactions is the polymer degree). The new approach may open the door to a new reliable low dimensional treatment of complex polymer reactions.}, language = {en} } @misc{Wulkow1990, author = {Wulkow, Michael}, title = {Numerical Treatment of Countable Systems of Ordinary Differential Equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4728}, number = {TR-90-08}, year = {1990}, abstract = {Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a full adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerkin approach as discretization of the stationary subproblems. The Galerkin method is based on orthogonal functions of a discrete variable , which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations can be assembled either by use of analytical properties of the orthogonal functions or numerically by a multilevel summation algorithm. The resulting algorithm CODEX is applied to many examples of technological interest, in particular from polymer chemistry.}, language = {en} } @article{DeuflhardNowakWulkow1990, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing}, volume = {14}, journal = {Computers in Chemical Engineering}, pages = {1249 -- 1258}, year = {1990}, language = {en} }