Algorithm Based on the Gradient-Hamilton Decomposition Theory of Vector Fields

Based on the gradient-Hamiltonian decomposition (GHD) theory of vector fields, an algorithm (called as GHD algorithm) is proposed in this paper. For the GHD algorithm, visual interpretations of the advantages in stability are given by using the eigenvalue curves. From the numerical results for linear decay systems, it reaches the conclusion that the GHD algorithm proposed in this paper has a better computational accuracy than other algorithms and presents a replication of long time qualitative properties of the underlying system.