In this paper, we have developed a new approach based on a combination of the Arnoldi and frontal methods, which is suitable for solving large sparse asymmetric and generalized complex eigenvalue problems. The new eigensolver seeks the most unstable eigen-solution in the Krylov subspace and makes use of the efficiency of the frontal solver developed for the finite element methods. The approach is used for a stability analysis of flows in a collapsible channel and is found to significantly improve the computational efficiency compared to the traditionally used QZ solver or a standard Arnoldi method. With the new approach, we are able to validate the previous results obtained either on a much coarser mesh or estimated from unsteady simulations. New neutral stability solutions of the system are also obtained which are beyond the limit of previously used methods.