Preserving conservative and dissipative properties of dynamical systems is desirable in numerical integration. To this end, we develop and implement numerical methods that preserve the exact rate of dissipation in certain qualitative properties of dissipatively perturbed constrained Hamiltonian systems, which are shown to be conformal symplectic. Projection methods based on exponential Runge–Kutta methods are proposed for such systems. These numerical schemes are shown to be constraint preserving, conformal invariants preserving, symmetric, and second-order accurate. It is shown that these structure-preserving methods can be further composed to obtain higher-order structure-preserving methods. Linear stability analysis is used to derive stability properties and conformal preservation of the phase-space area. Numerical experiments, including constrained oscillators and a damped Korteweg–de Vries partial differential equation, demonstrate the advantages of geometric integration and verify theoretical results.

在数值积分中，希望保留动力学系统的保守性和耗散性。为此，我们开发并实现了数值方法，这些方法在耗散扰动的受约束哈密顿系统的某些定性性质中保留了精确的耗散率，这些耗散扰动被证明是保形辛的。针对此类系统，提出了基于指数Runge–Kutta方法的投影方法。这些数值方案显示为约束保持，保形共形不变，对称和二阶精确。结果表明，可以进一步构成这些结构保留方法，以获得更高阶的结构保留方法。线性稳定性分析用于推导相空间区域的稳定性和保形性。数值实验