Scholarlink

This paper explores the selection rules for the step size of the Jacobi matrix in solving differential equations using difference quotient methods. Different step sizes are selected for several typical examples, and the Jacobi matrix is approximated using first-order central difference method and five-point central difference method, respectively. The approximated Jacobi matrix is compared with analytical form of the Jacobi matrix. Rules for selecting the optimal step size when using different difference quotient methods to solve different types of problems are analyzed and proposed, and strategies for selecting the optimal step size in practical calculations are also presented.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Study on the Optimal Step Size of Jacobi Matrix for Ordinary Differential Equations by Difference Quotient Method

  • 会议论文

  • 发表日期：

    2026年

查看全文
  • Haoxuan Yao,
  • Xianduo Liu,
  • Junjie Gu,
  • Zouzhou Yao

摘要

This paper explores the selection rules for the step size of the Jacobi matrix in solving differential equations using difference quotient methods. Different step sizes are selected for several typical examples, and the Jacobi matrix is approximated using first-order central difference method and five-point central difference method, respectively. The approximated Jacobi matrix is compared with analytical form of the Jacobi matrix. Rules for selecting the optimal step size when using different difference quotient methods to solve different types of problems are analyzed and proposed, and strategies for selecting the optimal step size in practical calculations are also presented.