王莹,单莹莹

• 1:黑龙江大学数学与统计学院

摘要(Abstract)：

提出了一种求解二维电报方程的高精度全离散格式。该方法在时间上采用Crank-Nicolson格式进行离散，在空间上运用Legendre-Galerkin谱方法进行逼近。通过严格的数学分析，建立了该格式在L_2和H_1范数意义下的最优误差估计。理论结果表明：时间离散具有二阶精度O(Δt~2);空间离散的收敛速率依赖于解的光滑程度，在H_1范数下达到O(N~(-m)),在H_1范数下为O(N~(1-m)),其中Δt为时间步长，N是多项式阶数，m表示解的正则性程度。数值试验结果与理论预测吻合良好，验证了所提方法的有效性。

关键词(KeyWords)： 误差估计;Crank-Nicolson格式;Legendre-Galerkin方法;二维电报方程

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金资助项目(12271128)

作者(Author): 王莹,单莹莹

DOI: 10.13482/j.issn1001-7011.2026.04.210

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