TY - JOUR T1 - Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $\theta$-Schemes and Their Stability JO - Journal of Computational Mathematics VL - 5 SP - 573 EP - 582 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8714.html KW - Incremental unknowns, Semi-implicit schemes, $θ$-Schemes, Stability. AB -

Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit $\theta$-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 $\theta$ is closed to $1/2$ even if we have variable coefficients.