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本文对非线性延迟波动方程建立了一个高效的二阶线性隐式差分格式。运用离散能量法，证明了差分格式在最大模意义下是无条件收敛的，其收敛阶为O(τ~2+h2)。数值结果验证了所提格式的精度和有效性。
Abstract：In this paper, we propose an efficient linearized implicit difference scheme for a class of nonlinear wave equations with delay. It is proved that the present scheme is unconditionally convergent with the order of O(τ~2+h2) in discrete maximum norm. At last, some numerical results are showcased to confirm the accuracy and efficiency of the developed scheme.
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基本信息:
DOI：10.14096/j.cnki.cn34-1334/n.2026.03.001
中图分类号:O241.3
引用信息:
[1]谢建强,潘琬笛,汪灿.一类非线性延迟波动方程的线性隐式差分格式[J].阜阳师范大学学报(自然科学版),2026,43(01):1-6+22.DOI:10.14096/j.cnki.cn34-1334/n.2026.03.001.
基金信息:
国家自然科学基金项目(12201005); 安徽省大学生创新训练项目(S202310357012,X202410357018)
2026-03-15
2026-03-15