Abstract: The exact solution of regular perturbation systems holds significant theoretical value but presents inherent challenges. This study constructs series solutions via the direct expansion method, determining coefficient terms through a recursive algorithm to establish asymptotic solutions for the system. The existence of solutions is rigorously proven using the contraction mapping theorem. Parameter sensitivity analysis reveals the error estimation formula. The proposed method combines theoretical rigor with engineering practicality and can be extended to nonlinear dynamics and boundary layer problems.