I have a nonlinear differential algebraic system in time arising from the weak formulation of coupled transient non-linear 1D problem. The system roughly looks like. M*x[n] = (A + c1*I) * x[n-1] + dt*N(x[n-1], w[n-1]) B*w[n] = B * w[n-1] + ddt*N2(x[n-1], w[n-1])Here all capital letter represents matrices. x(y,t) and w(y,t) are unknowns. N and N2 represents nonlinear part of the system.I was thinking of using initial guess for both w[n-1] and x[n-1] and then solve the resulting nonlinear algebraic system. Update the values of x[n-1] and w[n-1] and repeat the process. Would it work??Second should I take the time steps for 'w' and 'x' to be same. I guess this decision needs to come from the physical situation but looking this in prospective of numerical stability issues with time I need some guidance.Regards!!
suggestion needed for solution algorithim non-linear differntial algebraic system
nonlinear equations