Which method will be useful to solve nonlinear coupled PDEs??

I'm stuck in solving these integro nonlinear coupled pdes which I have attached along with the boundary conditions. Is there anyone who can help me out to solve these two equations. Thanks in advance!!

**Here the primes denotes the derivative w.r.t eta.

Answer 1

[Prasanna Gude]

You can solve the Nonlinear Partial Differential Equations using ‘solvepde’ function in MATLAB. You can also solve your problems by putting in the correct form for ‘Partial Differential Equation Toolbox’solvers.

Refer to the following link to know more about ‘solvepde’function:

https://in.mathworks.com/help/pde/ug/pde.pdemodel.solvepde.html

In order to know the steps involved in solving the problems using PDEModel Objects, refer to the following link:

https://in.mathworks.com/help/pde/ug/solve-problems-using-pdemodel-objects.html