Scholarlink

<p>We develop a&#xa0;quintic B‑spline discretization for nonlinear two-point boundary value problems with general linear boundary conditions. Using the consistency relations of quintic splines on a&#xa0;uniform grid, we derive a&#xa0;compact, nonlinear algebraic system for the nodes, which is solved by Newton-type iterations. The spline representation is reconstructed and used to compute accurate approximations of the solution and its derivatives in terms of explicit B‑spline formulas. The method is numerically tested on singular Lane-Emden-type equations and Bratu problems (including two solution modes). The numerical results confirm the expected high-order accuracy in the node solution and show that spline-based derivative recovery remains robust, providing performance comparable to the representative spline-collocation and finite difference methods reported in the literature.</p>

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

Approximation of solutions to nonlinear two-point boundary value problems using quintic splines

  • 期刊论文

  • 发表日期：

    2026年3月1日

查看全文
  • Tugal Zhanlav,
  • Renchin-Ochir Mijiddorj,
  • Yuriy S. Volkov

摘要

We develop a quintic B‑spline discretization for nonlinear two-point boundary value problems with general linear boundary conditions. Using the consistency relations of quintic splines on a uniform grid, we derive a compact, nonlinear algebraic system for the nodes, which is solved by Newton-type iterations. The spline representation is reconstructed and used to compute accurate approximations of the solution and its derivatives in terms of explicit B‑spline formulas. The method is numerically tested on singular Lane-Emden-type equations and Bratu problems (including two solution modes). The numerical results confirm the expected high-order accuracy in the node solution and show that spline-based derivative recovery remains robust, providing performance comparable to the representative spline-collocation and finite difference methods reported in the literature.