0

I am interested in solving the following system of ODEs

x′=2x+3y+z
y′=x−3y+2z
z′=x+2y−4z

with conditions at distinct times, even at time at infinity.

x(0)=1
y(0)=1
z(+inf)=0

I tried to google but it seems to be no method in PYTHON, MATLAB suitable for this system. Are there any ideas? Thanks!

Leonard Neon
  • 183
  • 1
  • 7
  • down-vote for no reason?! hix hix?! – Leonard Neon Mar 08 '21 at 14:46
  • Do you want to do something similar to [this](https://mathematica.stackexchange.com/questions/57262/how-to-solve-ode-with-boundary-at-infinity) or [this](https://stackoverflow.com/questions/32884557/solve-differential-equation-with-infinite-boundary-condition-in-matlab)? – Vicky Mar 08 '21 at 16:29
  • 1
    Please avoid cross-posting or make it obvious with a preference of where the answers should go. https://math.stackexchange.com/questions/4053768/numerically-solving-a-system-of-linear-odes-with-different-time-conditions – Lutz Lehmann Mar 08 '21 at 18:04
  • @Vicky thank for your help, they are not exactly the same as we have to consider a system here. I found that many libraries in both python and matlab are only available for system without conditions or one equation with conditions. – Leonard Neon Mar 09 '21 at 15:40
  • @LutzLehmann Sorry I will learn from experience! Thanks! – Leonard Neon Mar 09 '21 at 15:41

1 Answers1

2

I don't think this make sense, mathematically speaking. ODE solvers start from a set of initial conditions. There isn't necessarily a unique solution to an ODE when your constraints are not all defined at the same start time.

Imagine an ODE which converges to a steady-state condition no matter the initial condition. If all you hand the solver is the final condition (at infinity time), what info does it have to divine the initial conditions?

aosborne
  • 371
  • 1
  • 7