The paper presents a novel, unified analytical framework that establishes strong \(L^2\) -stability for a general class of semi-implicit spectral deferred correction (SISDC) time integrators coupled with discontinuous Galerkin (DG) spatial discretizations for linear partial differential equations. The SISDC method treats the non-stiff term explicitly and the stiff term implicitly. A key contribution is the introduction of refined temporal difference operators and identities specifically designed for SISDC. These new identities are the analytic engine that allows the symmetric implicit spatial operator to control the explicit component, enabling a unified stability analysis. Using this framework, we prove strong \(L^2\) -stability under a time-step restriction \(\tau \le \tau _0\) , where the constant \(\tau _0\) is independent of the spatial mesh size h. The theory applies to a wide family of SISDC schemes and multiple DG spatial discretizations, and numerical experiments are provided to validate the theoretical results.
