Christian Lubich (born 29 July 1959) is an Austrian mathematician, specializing in numerical analysis.
Christian Lubich (born 29 July 1959) is an Austrian mathematician, specializing in numerical analysis.
After secondary education at the Bundesrealgymnasium in Innsbruck, Lubich studied mathematics at the University of Innsbruck from 1977 to graduation with Magister degree in 1981. He was from 1979 to 1981 a student assistant in Innsbruck and from 1981 to 1983 a research associate in the Sonderforschungsbereich 123 Stochastische mathematische Modelle at the University of Heidelberg. [1] He received his doctorate in 1983 from the University of Innsbruck with dissertation Zur Stabilität linearer Mehrschrittverfahren für Volterra-Gleichungen (On stability of linear multistep methods for Volterra equations) [2] under Ernst Hairer and habilitated there in 1987. Lubich was from 1983 to 1987 a university assistant in Innsbruck, in 1986/87 an assistant at the University of Geneva, in 1987/88 a visiting professor at the IRMAR at the University of Rennes, and in 1988 a visiting professor at the University of Geneva. He was from 1991 to 1992 an assistant professor at ETH Zurich and from 1992 to 1994 a professor of applied mathematics at University of Würzburg. He is since 1994 a professor of numerical mathematics at the University of Tübingen. [1]
Lubich received in 2001 the Dahlquist Prize of the Society for Industrial and Applied Mathematics (SIAM) and in 1985 the Research Prize of the city of Innsbruck. [1] In 2018 at the International Congress of Mathematicians (ICM) in Rio de Janeiro, he was a plenary speaker with talk Dynamics, numerical analysis, and some geometry, written jointly with his former doctoral student Ludwig Gauckler and with Ernst Hairer. [3]
Lubich has been a member of the editorial board of Numerische Mathematik since 1995, of Ricerche di Matematica and of the IMA Journal of Numerical Analysis since 2006, of BIT Numerical Mathematics since 1996, and of SIAM Journal on Scientific Computing from 1996 to 2001. [1]
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals.
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary differential equations (ODEs) having a finite dimensional state vector. Four points may give a possible explanation of the popularity of DDEs:
In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations (ODE). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions. The difference between these solutions is then taken to be the error of the (fourth-order) solution. This error estimate is very convenient for adaptive stepsize integration algorithms. Other similar integration methods are Fehlberg (RKF) and Cash–Karp (RKCK).
In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (ODEs) with high accuracy and comparatively little computational effort. It is named after Roland Bulirsch and Josef Stoer. It is sometimes called the Gragg–Bulirsch–Stoer (GBS) algorithm because of the importance of a result about the error function of the modified midpoint method, due to William B. Gragg.
Randall J. LeVeque is a Professor of Applied Mathematics at University of Washington who works in many fields including numerical analysis, computational fluid dynamics, and mathematical theory of conservation laws. Among other contributions, he is lead developer of the open source software project Clawpack for solving hyperbolic partial differential equations using the finite volume method. With Zhilin Li, he has also devised a numerical technique called the immersed interface method for solving problems with elastic boundaries or surface tension.
Denis Louis Blackmore was an American mathematician and a full professor of the Department of Mathematical Sciences at New Jersey Institute of Technology. He was also one of the founding members of the Center for Applied Mathematics and Statistics at NJIT. Dr. Blackmore was mainly known for his many contributions in the fields of dynamical systems and differential topology. In addition to this, he had many contributions in other fields of applied mathematics, physics, biology, and engineering.
Ernst Hairer is a professor of mathematics at the University of Geneva known for his work in numerical analysis.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
William B. Gragg (1936–2016) ended his career as an Emeritus Professor in the Department of Applied Mathematics at the Naval Postgraduate School. He has made fundamental contributions in numerical analysis, particularly the areas of numerical linear algebra and numerical methods for ordinary differential equations.
Hans Jörg Stetter is a German mathematician, specializing in numerical analysis.
In numerical solution of differential equations, WENO methods are classes of high-resolution schemes. WENO are used in the numerical solution of hyperbolic partial differential equations. These methods were developed from ENO methods. The first WENO scheme was developed by Liu, Osher and Chan in 1994. In 1996, Guang-Sh and Chi-Wang Shu developed a new WENO scheme called WENO-JS. Nowadays, there are many WENO methods.
Marlis Hochbruck is a German applied mathematician and numerical analyst known for her research on matrix exponentials, exponential integrators, and their applications to the numerical solution of differential equations. She is a professor in the Institute for Applied and Numerical Mathematics at the Karlsruhe Institute of Technology.
Volker Ludwig Mehrmann is a German mathematician.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations.
Luigi Chierchia is an Italian mathematician, specializing in nonlinear differential equations, mathematical physics, and dynamical systems.
Gerhard Wanner is an Austrian mathematician.
Karl Kunisch is an Austrian mathematician.
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