The aim of this work is to apply a semi-implicit (SI) strategy to a sequence of one-dimensional time-dependent partial differential equations (PDEs) with high-order spatial derivatives which frequently give rise to stiff problems. We explore the SI approach in the context of implicit-explicit (IMEX) Runge–Kutta (RK), Rosenbrock-type, and IMEX linear multistep (LM) schemes. This strategy provides significant flexibility in handling such equations and enables the construction of simple, linearly implicit schemes without requiring Newton iterations. Furthermore, the SI schemes designed within this framework do not impose severe time step restrictions, which are typically necessary for stability when using explicit methods, i.e., ∆t= O(∆xk) for a k-th order (k ≥ 2) PDE. For spatial discretization, this approach is combined with finite difference schemes, such as WENO schemes. We demonstrate the effectiveness of the proposed methods through various applications to dissipative, dispersive, and biharmonic-type equations. Numerical experiments confirm that the proposed schemes are stable and can achieve optimal orders of accuracy.