Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows

The energy dissipation law and the maximum bound principle (MBP) are two important physical features of well-known Allen--Cahn equation. While some commonly used first-order time stepping schemes have turned out to preserve unconditionally both MBP for equation, restrictions on step size still needed existing second-order or even higher order in such simultaneous preservation. In this paper, we develop analyze novel first- linear numerical a class type gradient flows. Our combine generalized scalar auxiliary variable (SAV) approach exponential integrator with stabilization term, while standard central difference stencil is discretization spatial differential operator. We not only prove their unconditional preservation discrete setting, but also derive optimal temporal error estimates under fixed mesh. Numerical experiments carried demonstrate properties performance proposed schemes.