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Use the out put of ParametricNDSolve as initial condition?

GROUPS:

Hello,

I am trying to use ParametricNDSolve command to solve a system of differential equations. I have four system of differential equations that should be solved order by order and the out put of the first system is the initial condition for the second one and so on. The problem is that these system of equations are depended to a parameter thus i need to use ParametricNSDSolve command to solve them. Now I have a question, how does it possible to use the out put of the ParametricNDSolve as initial condition keeping it's parametric condition?

Thanks a lot,

Bests

POSTED BY: Mary Aghaei
Answer
5 months ago

You might consider getting a window on the parameter that you are using and specify the values of the parameters (in the window) you need while using ParametricNDSolve. If you have this the answer seems simple; you can solve the first differential equation for these set of parameters either using Table[NDSolve... ] etc or ParametricNDSolve and input these outputs as initial conditions for the next in a simple way.

POSTED BY: Gokul Hariharan
Answer
4 months ago

Thank you very much, but would you please explain what do you mean by having a window to specify the parameters while using ParametricNDSolve? I have these equations as in the attached file and I want to use the output of s2 and plot the functions g, f,p,q as a function of parameter "a" at t==60.

Thanks, Bests

Attachments:
POSTED BY: Mary Aghaei
Answer
4 months ago

Thank you very much, but would you please explain what do you mean by having a window to specify the parameters while using ParametricNDSolve? I have these equations as in the attached file and I want to use the output of s2 and plot the functions g, f,p,q as a function of parameter "a" at t==60.

Thanks, Bests

Attachments:
POSTED BY: Mary Aghaei
Answer
4 months ago

By window I meant what values will "a" typically take? For instance, 0<a<1. Specifying this can simplify the problem greatly. You could then sample values of "a" in this interval, say 10 to 100 points in this interval, or even more depending on what you desire to analyze.

There might be a direct alternative by keeping "a" totally unknown, I do not know of a method to do so. I haven't got a chance to go through the equations you sent yet, I'll tell you if I figure something when I look at it.

Thanks,

POSTED BY: Gokul Hariharan
Answer
4 months ago

Thank you very much,

The parameter "a" is not totally unknown. it has the values between 0.1 and 10 and if i want to get a suitable result i need to devide this interval to 0.01 steps. But unfortunately i can not get the point that how does it possible to solve the problem with specifying just the "a" interval. would please make a example for it?

Thanks,

POSTED BY: Mary Aghaei
Answer
4 months ago

Please find an example attached for a simpler problem.

Attachments:
POSTED BY: Gokul Hariharan
Answer
4 months ago

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