Software for Initial Value Problems

The code MEBDFDAE is designed to solve stiff initial value problems and differential algebraic equations. MEBDF is described in Hairer and Wanner [1].

Results have also been obtained on some difficult stiff test problems. These can be found in Hairer and Wanner, or on Hairer's home page. More test problems and a comparison of MEBDFDAE with some other codes can be found on the Amsterdam web page.

The drivers are the following:

The results are found in the corresponding .res files, for example for VDP the results are in DAEVDP.RES

Some extra problems are added. They are the B5 problem of DETEST with ALPHA=50,200,500,800,1000. The drivers are respectively

with the results in

Also we ran the ring modulator problem with CS=1e-9, 2e-12 [2, p.112]. The drivers are

and the results are

We also have results for some DAEs. We first ran the pendulum problem [2, p. 154] with INDEX=1, 2, 3. The results from MEBDFDAE are obtained by running PENDUL1.F, PENDUL2.F, PENDUL3.F, PENDUL4.F with the results in the corresponding files PENDUL1.RES, PENDUL2.RES, PENDUL3.RES, PENDUL4.RES. PENDUL4.F runs the problem as an ODE. We also ran some of the problems in the Amsterdam test set. These were:

ANDREWS SQUEEZING MECHANISM. For MEBDF the driver is ANDDRIV.F and results in ANDSQUEEZ.RES.
THE FEKETE PROBLEM. For MEBDF the driver is MEBFEKERUN.F and results in FEKEMEBDF.RES.
THE CAR AXIS PROBLEM. For MEBDF the driver is MEBDFCAR.F and results in MEBDFCAR.RES.
THE TRANSISTOR AMPLIFIER. For MEBDF the driver is TRANSRUN.F and results in TRANSRUN.RES.
THE BIT ADDING UNIT. For MEBDF with error control on constraints the driver is TBAMEBDF.F and results in TBAMEBDF.RES.
THE STIFF PENDULUM PROBLEM [3, p.120]. For MEBDF the driver is MEBDFSP.F and results in MEBDFSP.RES.

References

[1] E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer-Verlag 1996

[2] K.E. Brenan, S.L.Campbell and L.R. Pretzold, Numerical Solution of Initial Value Problems in Differential-Algebraic Equations, North Holland, 1989

[3] E. Hairer, C. Lubich and M. Roche, The Numerical Solution of Differential Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Mathematics, 1409, Springer Verlag 1989

[4] W.M. Lioen, J.J.B. de Swart and W.A. van der Veen, Test Set for IVP Solvers, CWI, Department of Mathematics, Amsterdam, Report NM-R9615, 1996

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Last updated April 17, 1997.

Jeff Cash (j.cash@ma.ic.ac.uk)

people have visited this page since April 1997.