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C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 خرداد 1405 اصل مقاله (1.12 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.68585.3326 | ||
| نویسنده | ||
| Gemeda Tolessa Lubo* | ||
| Department of Mathematics, Dembi Dollo University, Dambi Dollo, Ethiopia. | ||
| چکیده | ||
| This paper presents a $C^1$-conforming finite element method (FEM) for solving fourth-order ordinary differential equations (ODEs) using cubic Hermite basis functions. The proposed scheme inherently enforces $C^1$-continuity and accommodates both clamped and simply supported boundary conditions. A rigorous theoretical analysis demonstrates the method's stability and optimal convergence rates, achieving $\mathcal{O}(h^2)$ in the $H^2$-norm and $\mathcal{O}(h^4)$ in the $L^2$-norm. Numerical experiments validate the theoretical results, showing excellent agreement with exact solutions. The study underscores the efficacy of Hermite FEM for high-order BVPs, providing a robust and accurate computational framework. | ||
| کلیدواژهها | ||
| Hermite FEM؛ Fourth-order ODEs؛ $C^1$-conforming؛ Boundary value problems؛ Optimal convergences | ||
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آمار تعداد مشاهده مقاله: 63 تعداد دریافت فایل اصل مقاله: 76 |
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