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MathGroup Archive 2002

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problem with ndsolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg32886] problem with ndsolve
  • From: sahni mayank <sahnimayank at yahoo.com>
  • Date: Mon, 18 Feb 2002 05:22:06 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

hi all
i've been using ndsolve for some time and i'm facing a
problem involving coupling of 2 sets of differential
equations.the example below illustrates my problem and
i'm also attaching a copy of my program along with
this mail [attachments are not permitted in this group,
contact the author to receive it - moderator]:

sol1 = NDSolve[{
  y1'[t] == 0.5*k2 + k4*y2[t]*y3[t] - k10*y1[t]*y4[t],
  y2'[t] == k1 + k3 + k5*y1[t]*y1[t] - k4*y2[t]*y3[t],

  y3'[t] == k9*y3[t]*y1[t] - k4*y2[t]*y3[t] -
k8*y1[t]*y3[t]
and i specify the initial conditions,the working
precision etc which are:

StartingStepSize -> 0.000000000000000000001,
AccuracyGoal -> 13, 
PrecisionGoal -> 13,
WorkingPrecision -> 16, 
MaxSteps -> 100000000000000000000]



the program gives me a good output in terms of the
graphs i plot which are smooth and without
fluctuations


but as soon as i incorporate the 2nd set of
differential equations for eg:
sol1 = NDSolve[{
  y1'[t] == 0.5*k2 + k4*y2[t]*y3[t] - k10*y1[t]*y4[t],
  y2'[t] == k1 + k3 + k5*y1[t]*y1[t] - k4*y2[t]*y3[t],

  y3'[t] == k9*y3[t]*y1[t] - k4*y2[t]*y3[t] -
k8*y1[t]*y3[t]

s1'[t] == 0.5*k2 + k4*s2[t]*y3[t] - k10*s1t]*y4[t],
  s2'[t] == k1 + k3 + k5*s1[t]*y1[t] - k4*s2[t]*y3[t],

  s3'[t] == k9*s3[t]*y1[t] - k4*s2[t]*y3[t] -
k8*s1[t]*y3[t]

and solve the equations giving the earlier working
precison etc the program doesn;t give me a result and
if i decrease these parameters(lower precison and
steps) the graphs for eg y1[t] or y3[t] show a wide
fluctuation.

only the differential equations in S are dependent on
Y.

is there any way to work around this problem so that
when i evaluate the differential equations of y and s
simultaneously i get smooth plots which will make
sense.is there any other function(instead of NDSOLVE)
which is more effective is solving stiff differential
equations.

Mayank.


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