Stability and Error Analysis of IMEX SAV Schemes for the Magneto-Hydrodynamic Equations

We construct and analyze first- second-order implicit-explicit schemes based on the scalar auxiliary variable approach for magneto-hydrodynamic equations. These are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, unconditionally energy stable. derive rigorous error estimates velocity, pressure, magnetic field first-order scheme in two-dimensional case without any condition step. Numerical examples presented to validate proposed schemes.