deTestSet (version 1.0)

ring: The Ring Modulator Problem, Electrical Circuit Analysis, ODE

Description

The probelm describes the behavior of the ring modulator, an electrical circuit.

The type of the problem depends on the parameter Cs. If Cs is not equal 0, then it is a stiff system of 15 non-linear ordinary differential equations.

For Cs = 0 we have a DAE of index 2, consisting of 11 differential equations and 4 algebraic equations. The numerical results presented here refer to Cs = 2 e-12. The problem has been taken from [KRS92], where the approach of Horneber [Hor76] is followed. The parallel-IVP-algorithm group of CWI contributed this problem to the test set. The software part of the problem is in the file ringmod.f available at [MM08].

Usage

ring (times = seq(0, 0.001, by = 5e-06), yini = NULL, 
      dyini = NULL, parms = list(), method = "mebdfi", 
       atol = 1e-8, rtol = 1e-8, maxsteps = 1e+06, ...)

Arguments

yini

the initial (state) values for the DE system. If y has a name attribute, the names will be used to label the output matrix.

dyini

the initial derivatives of the state variables of the DE system.

times

time sequence for which output is wanted; the first value of times must be the initial time.

parms

list of parameters that overrule the default parameter values

method

the solver to use

atol

absolute error tolerance, either a scalar or a vector, one value for each y.

rtol

relative error tolerance, either a scalar or a vector, one value for each y,

maxsteps

maximal number of steps per output interval taken by the solver

...

additional arguments passed to the solver .

Value

• A matrix of class deSolve with up to as many rows as elements in times and as many columns as elements in yini, plus an additional column (the first) for the time value.

  There will be one row for each element in times unless the solver returns with an unrecoverable error. If yini has a names attribute, it will be used to label the columns of the output value.

Details

The default parameters are: M1 = 0.36, M2 = 0.151104, M3 = 0.075552, L1 = 0.15, L2 = 0.30, J1 = 0.002727, J2 = 0.0045339259, EE = 0.20e12, NUE= 0.30, BB = 0.0080, HH = 0.0080, RHO= 7870.0, GRAV= 0.0, OMEGA = 150.0 There are two default initial conditions - set with options(ini=x)

References

http://www.dm.uniba.it/~testset

[Hor76] E.H. Horneber. Analyse nichtlinearer RLCU-Netzwerke mit Hilfe der gemischten Potentialfunktion mit einer systematischen Darstellung der Analyse nichtlinearer dynamischer Netzwerke. PhD thesis, Universitat Kaiserslautern, 1976.

[KRS92] W. Kampowski, P. Rentrop, and W. Schmidt. Classiffcation and numerical simulation of electric circuits. Surveys on Mathematics for Industry, 2(1):23--65, 1992.

[MM08] F. Mazzia and C. Magherini. Test Set for Initial Value Problem Solvers, release 2.4. Department of Mathematics, University of Bari and INdAM, Research Unit of Bari, February 2008

Examples

out <- ring()
plot(out, col = "darkblue", lwd = 2)
mtext(side = 3, line = -1.5, "RING modulator",cex = 1.25, outer = TRUE)

# compare with reference solution
max(abs(out[nrow(out),-1]- reference("ring")))