Scholarlink

<p>In this article, we introduce a new hybrid block collocation method (NHBCM) using polynomial approximation for solving two-dimensional elliptic partial differential equations (PDEs). The theoretical analysis demonstrates that the NHBCM achieves fifth-order accuracy, highlighting its robustness in stability and convergence. We validate the effectiveness of the NHBCM through a series of test problems, showcasing its practical applications. The comparison results indicate that the NHBCM provides significantly more efficient solutions for both linear and nonlinear elliptic model PDEs than other numerical methods used for comparison, thereby validating the superior performance of the NHBCM.</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

A new hybrid block collocation method for solving elliptic PDEs

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月16日

查看全文
  • Mufutau Ajani Rufai,
  • Salvatore Filippone,
  • Higinio Ramos,
  • Giovanni Modanese

摘要

In this article, we introduce a new hybrid block collocation method (NHBCM) using polynomial approximation for solving two-dimensional elliptic partial differential equations (PDEs). The theoretical analysis demonstrates that the NHBCM achieves fifth-order accuracy, highlighting its robustness in stability and convergence. We validate the effectiveness of the NHBCM through a series of test problems, showcasing its practical applications. The comparison results indicate that the NHBCM provides significantly more efficient solutions for both linear and nonlinear elliptic model PDEs than other numerical methods used for comparison, thereby validating the superior performance of the NHBCM.