This paper presents a semi-analytical method in the Hamiltonian system
combined with the finite element method. Second-order non-homogeneous
elliptic partial differential equations are taken to illustrate the f
ormulation. One numerical example of the proposed method is also given
and compared with the analytical method, the Ritz method, the finite
strip method and the finite element method. The proposed method gives
more accurate results for the co-state variable. It is an attempt to f
ormulate the finite strip method in state space.