一类Kirchhoff方程的解的存在性及数值解法
Existence Results and Numerical Approximations for a Class of Kirchhoff Equation
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作者信息
摘要
针对一类Kirchhoff方程的解的存在性和数值解法进行研究.首先,引入1个参数将原问题转化为等价的方程来讨论解的存在性.其次,提出了方程的迭代解法,分析了迭代解法的收敛性.然后,基于迭代解法和二阶差分格式对方程进行求解,给出了相应的误差分析.最后,利用数值算例验证了理论分析的结果.
Abstract
In this paper,the existence and numerical solutions of a class of Kirchhoff equations are studied.Firstly,a parameter is introduced to transform the original problem into an equivalent equation to discuss the existence of the solution.Secondly,a iterative method of the equation is given,and the convergence of the iterative method is analyzed.Then,based on the iterative method,the second-order difference scheme and error analysis for the Kirchhoff equation are also derived.Finally,results of numerical experiments confirm the efficiency of the proposed method are given.
关键词
Kirchhoff方程/解的存在性/迭代法/差分格式/误差分析Key words
Kirchhoff equation/Existence of solutions/Iterative method/Difference scheme/Error analysis引用本文复制引用
出版年
2024
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