@article{DeuflhardPotra1992, author = {Deuflhard, Peter and Potra, Florian}, title = {Asymptotic Mesh Independence for Newton-Galerkin Methods via a Refined Mysovskii Theorem}, volume = {29}, journal = {SIAM J. Numer. Anal.}, number = {5}, pages = {1395 -- 1412}, year = {1992}, language = {en} } @article{DeuflhardSautter1980, author = {Deuflhard, Peter and Sautter, W.}, title = {On Rank-Deficient Pseudoinverses}, volume = {29}, journal = {Lin. Alg. Appl.}, pages = {91 -- 111}, year = {1980}, language = {en} } @article{DeuflhardHeindl1979, author = {Deuflhard, Peter and Heindl, G.}, title = {Affine Invariant Convergence Theorems for Newton's Method and Extensions to Related Methods}, volume = {16}, journal = {SIAM J. Numer. Anal.}, pages = {1 -- 10}, year = {1979}, language = {en} } @incollection{DeuflhardHeroth1996, author = {Deuflhard, Peter and Heroth, J{\"o}rg}, title = {Dynamic dimension reduction in ODE models}, booktitle = {Scientific computing in chemical engineering}, editor = {et al. Keil, Frerich}, publisher = {Berlin: Springer-Verlag}, pages = {29 -- 43}, year = {1996}, language = {en} } @inproceedings{DeuflhardHerothMaas1996, author = {Deuflhard, Peter and Heroth, J{\"o}rg and Maas, Ulrich}, title = {Towards Dynamic Dimension Reduction in Reactive Flow Problems}, booktitle = {Proc. 3rd Workshop on Modelling of Chemical Reaction Systems}, address = {Heidelberg}, year = {1996}, language = {en} } @inproceedings{DeuflhardHegeSeebass2000, author = {Deuflhard, Peter and Hege, Hans-Christian and Seebass, Martin}, title = {Progress Towards a Combined MRI Hyperthermia System}, booktitle = {Proc. Second Int. Congress HIGH CARE 2000, Bochum}, editor = {Gr{\"o}nemeyer, W.}, year = {2000}, language = {en} } @book{DeuflhardHohmann2002, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik. I}, edition = {3}, publisher = {de Gruyter Lehrbuch. Berlin: de Gruyter}, year = {2002}, language = {en} } @book{DeuflhardHohmann2003, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerical analysis in modern scientific computing. An introduction. 2nd revised ed.}, volume = {43}, journal = {Texts in Applied Mathematics}, publisher = {New York, NY: Springer}, year = {2003}, language = {en} } @article{DeuflhardHochmuth2004, author = {Deuflhard, Peter and Hochmuth, Reinhard}, title = {Multiscale analysis of thermoregulation in the human microvascular system}, volume = {27}, journal = {Math. Methods Appl. Sci.}, number = {8}, publisher = {Wiley Verlag}, pages = {971 -- 989}, year = {2004}, language = {en} } @book{DeuflhardHohmann1991, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerische Mathematik I. Eine algorithmisch orientierte Einf{\"u}hrung}, publisher = {de Gruyter Lehrbuch,Berlin}, year = {1991}, language = {en} } @book{DeuflhardHohmann1995, author = {Deuflhard, Peter and Hohmann, Andreas}, title = {Numerical analysis. A 1st course in scientific computation. Transl. from the German by F. A. Potra and F. Schulz}, publisher = {de Gruyter Textbook. Berlin: De Gruyter}, year = {1995}, language = {en} } @article{DeuflhardHuisingaFischeretal.2000, author = {Deuflhard, Peter and Huisinga, Wilhelm and Fischer, Alexander and Sch{\"u}tte, Christof}, title = {Identification of Almost Invariant Aggregates in Reversible Nearly Uncoupled Markov Chains}, volume = {315}, journal = {Lin. Alg. Appl.}, pages = {39 -- 59}, year = {2000}, language = {en} } @incollection{DeuflhardWeber2005, author = {Deuflhard, Peter and Weber, Marcus}, title = {Robust Perron Cluster Analysis in Conformation Dynamics}, volume = {398}, booktitle = {Lin. Alg. Appl. - Special Issue on Matrices and Mathematical Biology}, publisher = {Elsevier Journals}, address = {Germany}, pages = {161 -- 184}, year = {2005}, language = {en} } @phdthesis{Deuflhard1968, author = {Deuflhard, Peter}, title = {Stimulierte Brillouinstreuung in Germanium bei 10.6 μ}, address = {Physics Dept.}, year = {1968}, language = {en} } @phdthesis{Deuflhard1972, author = {Deuflhard, Peter}, title = {Ein Newton-Verfahren bei fastsingul{\"a}rer Funktionalmatrix zur L{\"o}sung von nichtlinearen Randwertaufgaben mit der Mehrzielmethode}, address = {Math. Institute University of Cologne}, year = {1972}, language = {en} } @phdthesis{Deuflhard1976, author = {Deuflhard, Peter}, title = {A Stepsize Control for Continuation Methods with Special Application to Multiple Shooting Techniques}, address = {Math. Institute, Munich University of Technology}, year = {1976}, language = {en} } @misc{Deuflhard2000, author = {Deuflhard, Peter}, title = {Therapieplanung an virtuellen Krebspatienten}, publisher = {M. Aigner, E. Behrends (eds.): Alles Mathematik. Von Pythagoras zum CD-Player. Vieweg Verlag, pp. 22-30}, year = {2000}, language = {en} } @misc{Deuflhard2003, author = {Deuflhard, Peter}, title = {Maler, M{\"o}rder, Mathematiker}, publisher = {Gegenworte: Der Mythos und die Wissenschaft. Berlin-Brandenburgische Akademie der Wissenschaften (BBAW), 12. Heft, pp. 25-30}, year = {2003}, language = {en} } @misc{Deuflhard2003, author = {Deuflhard, Peter}, title = {Maler, M{\"o}rder, Mathematiker}, publisher = {Mitteilungen der Deutschen MathematikerVereinigung (DMV), pp. 16-21, Heft 4}, year = {2003}, language = {en} } @misc{Deuflhard2005, author = {Deuflhard, Peter}, title = {Pittori, assassini, matematici}, publisher = {M. Manaresi (ed.), Matematica e Cultura in Europa. Springer-Verlag Italia, pp. 145-155}, year = {2005}, language = {en} } @misc{Deuflhard1980, author = {Deuflhard, Peter}, title = {Linear and nonlinear least squares computing in view of control applications}, publisher = {Sonderforschungsbereich 123, Stochastische Mathematische Modelle. Universit{\"a}t Heidelberg}, pages = {85 -- 92}, year = {1980}, language = {en} } @misc{Deuflhard1998, author = {Deuflhard, Peter}, title = {Mathematics in Berlin}, editor = {et al. Begehr, H.}, publisher = {Basel: Birkh{\"a}user}, pages = {183 -- 184}, year = {1998}, language = {en} } @incollection{Deuflhard2000, author = {Deuflhard, Peter}, title = {Differential Equations in Technology and Medicine. Computational Concepts, Adaptive Algorithms, and Virtual Labs}, volume = {1739}, booktitle = {Computational Mathematics Driven by Industrial Applications}, publisher = {Springer-Verlag}, pages = {69 -- 125}, year = {2000}, language = {en} } @incollection{Deuflhard2003, author = {Deuflhard, Peter}, title = {A Comparison of Related Concepts in Computational Chemistry and Mathematics}, volume = {88}, booktitle = {Chemisty and Mathematics}, number = {330}, pages = {51 -- 66}, year = {2003}, language = {en} } @incollection{Deuflhard2003, author = {Deuflhard, Peter}, title = {From Molecular Dynamics to Conformational Dynamics in Drug Design}, booktitle = {Trends in Nonlinear Analysis}, editor = {et al. Kirkilionis, Markus}, publisher = {Springer Verlag Berlin}, pages = {269 -- 288}, year = {2003}, language = {en} } @article{Deuflhard2004, author = {Deuflhard, Peter}, title = {bookreview}, volume = {106}, journal = {Annual Report DMV}, pages = {43}, year = {2004}, language = {en} } @book{Deuflhard2004, author = {Deuflhard, Peter}, title = {Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms}, journal = {Springer Series in Computational Mathematics}, publisher = {Springer}, year = {2004}, language = {en} } @book{Deuflhard2006, author = {Deuflhard, Peter}, title = {Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms}, journal = {Springer Series in Computational Mathematics}, publisher = {Springer}, year = {2006}, language = {en} } @article{Deuflhard1974, author = {Deuflhard, Peter}, title = {A Modified Newton Method for the Solution of Ill-Conditioned Systems of Nonlinear Equations with Application to Multiple Shooting}, volume = {22}, journal = {Numer. Math.}, pages = {289 -- 315}, year = {1974}, language = {en} } @incollection{Deuflhard1975, author = {Deuflhard, Peter}, title = {A Relaxation Strategy for the Modified Newton Method}, volume = {477}, booktitle = {Optimization and Optimal Control}, publisher = {Springer}, pages = {59 -- 73}, year = {1975}, language = {en} } @article{Deuflhard1976, author = {Deuflhard, Peter}, title = {On Algorithms for the Summation of Certain Special Functions}, volume = {17}, journal = {Computing}, pages = {37 -- 48}, year = {1976}, language = {en} } @article{Deuflhard1977, author = {Deuflhard, Peter}, title = {A Summation Technique for Minimal Solutions of Linear Homogeneous Difference Equations}, volume = {18}, journal = {Computing}, pages = {1 -- 13}, year = {1977}, language = {en} } @inproceedings{DeuflhardApostolescu1978, author = {Deuflhard, Peter and Apostolescu, Victor}, title = {An Underrelaxed Gauss-Newton Method for Equality Constrained Nonlinear Least Squares Problems}, volume = {7}, booktitle = {Optimization Techniques, Proc. 8th IFIP Conf., W{\"u}rzburg 1977, part 2}, editor = {Stoer, J.}, publisher = {Springer}, pages = {22 -- 32}, year = {1978}, language = {en} } @inproceedings{Deuflhard1979, author = {Deuflhard, Peter}, title = {Nonlinear Equation Solvers in Boundary Value Problem Codes}, volume = {74}, booktitle = {Proc. Working Conf. on Codes for BVPs in ODEs, Houston/Texas 1978}, editor = {Childs, B.}, publisher = {Springer}, pages = {40 -- 66}, year = {1979}, language = {en} } @article{Deuflhard1979, author = {Deuflhard, Peter}, title = {A study of extrapolation methods based on multistep schemes without parasitic solutions}, volume = {30}, journal = {J.App.Math.Phys.(ZAMP)}, pages = {177 -- 189}, year = {1979}, language = {en} } @article{Deuflhard1979, author = {Deuflhard, Peter}, title = {A Stepsize Control for Continuation Methods and its Special Application to Multiple Shooting Techniques}, volume = {33}, journal = {Numer. Math.}, pages = {115 -- 146}, year = {1979}, language = {en} } @incollection{Deuflhard1980, author = {Deuflhard, Peter}, title = {Recent Advances in Multiple Shooting Techniques}, booktitle = {Computational Techniques for Ordinary Differential Equations}, publisher = {London: Academic Press}, pages = {217 -- 272}, year = {1980}, language = {en} } @misc{DeuflhardZachow2012, author = {Deuflhard, Peter and Zachow, Stefan}, title = {Mathematische Therapie- und Operationsplanung}, publisher = {Berliner Wirtschaftsgespr{\"a}che e.V.}, address = {Berlin}, pages = {89 -- 90}, year = {2012}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2010, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {More Mathematics into Medicine!}, booktitle = {Production Factor Mathematics}, publisher = {Springer}, pages = {357 -- 378}, year = {2010}, language = {en} } @article{WeiserZachowDeuflhard2010, author = {Weiser, Martin and Zachow, Stefan and Deuflhard, Peter}, title = {Craniofacial Surgery Planning Based on Virtual Patient Models}, volume = {52}, journal = {it - Information Technology}, number = {5}, publisher = {Oldenbourg Verlagsgruppe}, doi = {10.1524/itit.2010.0600}, pages = {258 -- 263}, year = {2010}, language = {en} } @incollection{DeuflhardDoesselLouisetal.2008, author = {Deuflhard, Peter and D{\"o}ssel, Olaf and Louis, Alfred and Zachow, Stefan}, title = {Mehr Mathematik wagen in der Medizin}, booktitle = {acatech diskutiert, Produktionsfaktor Mathematik - Wie Mathematik Technik und Wirtschaft bewegt}, publisher = {Springer}, doi = {10.1007/978-3-540-89435-3}, pages = {435 -- 459}, year = {2008}, language = {en} } @article{ZachowDeuflhard2008, author = {Zachow, Stefan and Deuflhard, Peter}, title = {Computergest{\"u}tzte Planung in der kraniofazialen Chirurgie}, journal = {Face 01/08, Int. Mag. of Orofacial Esthetics}, publisher = {Oemus Journale Leipzig}, pages = {43 -- 49}, year = {2008}, language = {en} } @inproceedings{ZachowHegeDeuflhard2004, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Computergest{\"u}tzte Operationsplanung in der Gesichtschirurgie}, booktitle = {Proc. VDE Kongress 2004 - Innovationen f{\"u}r Menschen, Band 2, Fachtagungsberichte DGBMT - GMM - GMA}, pages = {53 -- 58}, year = {2004}, language = {en} } @article{HaberlHellZoeckleretal.2004, author = {Haberl, Hannes and Hell, Bertold and Z{\"o}ckler, Maja and Zachow, Stefan and Lamecker, Hans and Sarrafzadeh, Asita and Riecke, B. and Langsch, Wolfgang and Deuflhard, Peter and Bier, J{\"u}rgen and Brock, Mario}, title = {Technical aspects and results of surgery for craniosynostosis}, volume = {65}, journal = {Zentralblatt f{\"u}r Neurochirurgie}, number = {2}, pages = {65 -- 74}, year = {2004}, language = {en} } @article{ZachowHegeDeuflhard2005, author = {Zachow, Stefan and Hege, Hans-Christian and Deuflhard, Peter}, title = {Maxillofacial surgery planning with 3D soft tissue prediction - modeling, planning, simulation}, journal = {2. Int. Conf. on Advanced Digital Technology in Head and Neck Reconstruction, Abstract 33}, address = {Banff, Alberta, CA}, pages = {64}, year = {2005}, language = {en} } @book{DeuflhardRoeblitz2015, author = {Deuflhard, Peter and R{\"o}blitz, Susanna}, title = {A guide to numerical modelling in systems biology}, volume = {12}, publisher = {Springer}, isbn = {978-3-319-20058-3}, doi = {10.1007/978-3-319-20059-0}, year = {2015}, language = {en} } @article{MoualeuNgangueRoeblitzEhrigetal.2015, author = {Moualeu-Ngangue, Dany Pascal and R{\"o}blitz, Susanna and Ehrig, Rainald and Deuflhard, Peter}, title = {Parameter Identification in a Tuberculosis Model for Cameroon}, journal = {PLOS ONE}, doi = {10.1371/journal.pone.0120607}, year = {2015}, abstract = {A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.}, language = {en} } @misc{SteinWeberScharkoietal.2013, author = {Stein, Christoph and Weber, Marcus and Scharkoi, Olga and Deuflhard, Peter}, title = {Method and system for identifying compounds that bind and preferably activate a target opioid receptor in a pH-dependent manner}, journal = {European Patent Application, Bulletin 2013/28}, year = {2013}, language = {en} } @misc{DeuflhardWeber2014, author = {Deuflhard, Peter and Weber, Marcus}, title = {Mathematics without pain}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, doi = {10.4171/137}, pages = {26 -- 28}, year = {2014}, language = {en} } @misc{BockmayrSiebertRoeblitzetal.2014, author = {Bockmayr, Alexander and Siebert, Heike and R{\"o}blitz, Susanna and Sch{\"u}tte, Christof and Deuflhard, Peter}, title = {Advanced mathematical modeling in systems biology}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutela, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {29 -- 44}, year = {2014}, language = {en} } @misc{DeuflhardKornhuberSanderetal.2014, author = {Deuflhard, Peter and Kornhuber, Ralf and Sander, Oliver and Schiela, Anton and Weiser, Martin}, title = {Mathematics cures virtual patients}, volume = {1}, journal = {MATHEON-Mathematics for Key Technologies}, editor = {Deuflhard, Peter and Gr{\"o}tschel, Martin and H{\"o}mberg, Dietmar and Horst, Ulrich and Kramer, J{\"u}rg and Mehrmann, Volker and Polthier, Konrad and Schmidt, Frank and Sch{\"u}tte, Christof and Skutella, Martin and Sprekels, J{\"u}rgen}, publisher = {European Mathematical Society}, pages = {7 -- 25}, year = {2014}, language = {en} } @article{MoualeuNgangueWeiserEhrigetal.2015, author = {Moualeu-Ngangue, Dany Pascal and Weiser, Martin and Ehrig, Rainald and Deuflhard, Peter}, title = {Optimal control for a tuberculosis model with undetected cases in Cameroon}, volume = {20}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {3}, doi = {10.1016/j.cnsns.2014.06.037}, pages = {986 -- 1003}, year = {2015}, abstract = {This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 \% in 10 years.}, language = {en} }