Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $θ$-Schemes and Their Stability (Journal of Computational Mathematics, 2007)
Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit $θ$-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when $θ$ is closed to $1/2$ even if we have variable coefficients.
Keywords: Incremental unknowns; Semi-implicit schemes; $θ$-Schemes; Stability.