Hi

Yes as it's, the system is not easy and requires so much work and tears. I will summarize my question to make it easier to understand. So I have system of coupled pdes. The unknown variables are dependent on time and space: du/dt=f(u'', u', u, v'', v', v, s'', s', s), dv/dt=f(u'', u', u, v'', v', v, s'', s', s), ds/dt=f(u'', u', u, v'', v', v, s'', s', s). So I have used finite difference method to discretize the derivative terms. However, since they are nonlinear, I should choose an iterative method to compute the solution. I was thinking to implement Picard method, but skeptical that the iteration will never reach the minimum tolerance between the solution and initial guesses. So which method would you recommend to use?

Thank you