Numerische Mathematik II - Numerical Analysis II (SoSe 2014)

Team:


	Name	Office	Office hours	Phone	E-Mail

Lecturer:	Andreas Steinbrecher	MA 463	Wed 10-11	314-79177	anst@math.tu-berlin.de
Assistant:	Jeroen Stolwijk	MA 462	Mon 12-14 in MA241	314-23439	stolwijk@math.tu-berlin.de

Lecture and Venue:


	Time	Room	Comments

Lecture:	Tue 14-16	MA 650
	Thu 14-16	MA 649

Tutorial:	Mon 14-16	MA 841

News:

Contents:

Many physical processes are modeled using differential equations. In this course, modeling and numerical treatment of initial and
boundary value problems for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) will be covered.
We will therefore investigate one-step methods, extrapolation methods, and multi-step methods numerically.

Exercise Sheets:


	Online on	Theoretical HW due	Programming HW 1st chance	Programming HW 2nd chance	Programming plots

Sheet 01	April 17	--	April 28	May 5	--
Sheet 02	April 24	May 6	--	--	--
Sheet 03	May 2	May 13	May 12	May 19	plot
Sheet 04	May 8	May 20	--	--	--
Sheet 05	May 15	May 27	May 22	June 2	plot
Sheet 06	May 20	June 3	--	--	--
Sheet 07	May 23	June 10	June 16	June 23	plot
Sheet 08	June 11	June 24	--	--	--
Sheet 09	June 20	July 3	June 30	July 7	plot
Sheet 10	June 26	July 10	--	--	--
Sheet 11	July 4	--	--	--	--
Sheet 12	July 11	--	--	--	--

Material:

Examples of explicit Runge-Kutta methods [ExpRKMethods.pdf].
Examples of the Linear spring-damper system [exp_SteifTestrechnung.pdf].
Examples of explicit Runge-Kutta methods together with their stability regions [exp_StabRegionsRKexpl.pdf].
Examples of implicit Runge-Kutta methods together with their stability regions [exp_StabRegionsRKimpl.pdf].
Examples of instable behaviour of multistep methods [exp_instMSV.pdf].
Examples of convergence behavior of multistep methods [exp_ConvMidPointRule.pdf].
Examples of stability regions of Adams-methods [exp_StabRegionsAdams.pdf].
Examples of stability regions of predictor-corrector methods [exp_StabRegionsPECE.pdf].
Examples of stability regions of BDF-methods [exp_StabRegionsBDF.pdf].
Andreas' presentation on hidden constraints [MathPendNumRes.pdf].

Literature:

[DeuB94]	P. Deuflhard und F. Bornemann, Numerische Mathematik II, de Gruyter, 1994.
[HaiNW00]	E. Hairer, S.P.Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, Springer, 2000.
[HaiW10]	E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Springer, 2010.
[Heu06]	H. Heuser: Gewöhnliche Differentialgleichungen, Vieweg+Teubner Verlag, 2006.
[StoB]	J. Stoer, R. Bulirsch: Numerische Mathematik II. Springer-Verlag
[StrWP12]	K. Strehmel, R. Weiner, H. Podhaisky: Numerik gewöhnlicher Differentialgleichungen. Springer, 2012

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Jeroen Stolwijk 15.07.2014