Convergent Stochastic Scalar Auxiliary Variable Method for Numerical Approximation of Nonlinear Stochastic Partial Differential Equations

The author proposes a new convergent stochastic scalar auxiliary variable (SSAV) method for the numerical approximation of nonlinear stochastic partial differential equations, using the stochastic Allen-Cahn equation as a prototype. The SSAV method allows for the derivation of linear, unconditionally stable, and convergent fully discrete schemes.