Discussion Forum

Hi:

I am trying to solve an 1D integro-differential equation. The problem equation is:

, in the domain ,

where . The boundary conditions are .

I have used the dest() operator and intop1() function. To solve this I have taken two approaches:

1. Using the stationary solver, as the problem is at steady state. The results are very small and close to zero everywhere, the trivial solution.

2. Using the time dependent solver, and simulating for t up to 10, such the time dependence effect is reduced relatively. In this case, the solution is extremely fluctuating (within small values) and shows an extremely high value at x = 0.

I have considered the element order to be quadratic. I have also tried with the linear. The comsol model file (using v5.6) can be downloaded from this link: https://www.dropbox.com/s/ejww38j1350ddaj/try6_28mar2021.mph?dl=0

Please advise on how to find a non-trivial solution and if there is anything I am doing it wrong. Any relevant document or information can be helpful. Note that I have already gone through the information from these helpful pages:

https://www.comsol.co.in/model/an-integro-partial-differential-equation-700

https://www.comsol.com/blogs/integrals-with-moving-limits-and-solving-integro-differential-equations/

The problem here is slightly more complex than the above two references, as it involves differentiation of the integrated quantity inside the equation.

Sourav