二维变系数抛物型方程的一个高阶ADI差分格式

摘要

A high accuracy alternation direction implicit scheme (ADI) for solving the two-dimensional parabolic equations is presented, and the scheme is absolutely stable and the truncation error is O(τ2+h4). The experiments show the scheme is effective and advantage, and the theory is right by a numerical example.%针对二维变系数抛物型方程，构造出了一个高精度、恒稳定的交替方向隐式（ADI）差分格式，格式的截断误差阶达O（τ2+h4）。通过数值实验，验证了理论分析的正确性和差分格式的精确性与有效性。