论文标题
矩形域上2D半线性热方程的放松/有限差异化离散化
A Relaxation/Finite Difference discretization of a 2D Semilinear Heat Equation over a rectangular domain
论文作者
论文摘要
我们考虑了矩形域上半线性的二维热方程的初始和差异边界值问题。该问题由C. Besse（C. R.Acad。Sci。Parissér。I，第326卷（1998年））提出的放松方案的版本离散化，用于非线性Schrödinger方程，并通过标准的二阶有限差差异方法在空间中为空间而言。所提出的方法无条件地拟合，并通过证明最佳的二阶误差估计值，从而确定其收敛性。
We consider an initial and Dirichlet boundary value problem for a semilinear, two dimensional heat equation over a rectangular domain. The problem is discretized in time by a version of the Relaxation Scheme proposed by C. Besse (C. R. Acad. Sci. Paris Sér. I, vol. 326 (1998)) for the nonlinear Schrödinger equation and in space by a standard second order finite difference method. The proposed method is unconditionally well-posed and its convergence is established by proving an optimal second order error estimate allowing a mild mesh condition to hold.
