A family of novel structure-preserving schemes are presented for numerically solving conservative/dissipative systems. These schemes are constructed by using the relaxation idea in the time discretization. After obtaining the relaxation parameter, it is shown that the methods can be arbitrarily high-order accurate, linearly implicit and keep the original discrete energy conserved/stable. Numerical comparisons with various typical structure-preserving schemes are presented. The numerical results show that the proposed schemes are highly competitive and effective.
