Hi Reza, Initial conditions are usually know by user. Depending to your nonlinear terms, it might help to look at the phase plots of your equation and come up with ranges of u and \dot{u} for specific outcomes.

Romik Khajehtourian

Hi Romik

Tanks for answering, but the solutions are very sensetive to initial condition.

I think I should use shooting methods for it but I dont know how.

regards

Hi Reza,

I still think phase plot will help you. By phase (u vs \dot{u}) plot you can predict the behavior of you pde for variety of initial condition, and probably you will find a narrow band in the plot that you are talking about helping you to choose right values. I suggest you give it a try, or share your equation so I can comment further. Here is a link for matheatica code examples:

http://www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch2/portrait.html

Regarding the shooting method, I suggest to use mathematica again:

https://reference.wolfram.com/language/tutorial/NDSolveBVP.html

Romik Khajehtourian

Hi Romik

I’ll use these puns you suggested into my work, and thanks again for your kelp.

Best