Numerical Investigation of Fourth-Order Boundary Value Problems Using the Finite Difference Method

Abstract

In this work, the finite difference method (FDM) is applied to derive numerical approximations for fourth-order boundary value problems (BVPs) governed by linear ordinary differential equations (LODEs). To assess the effectiveness of the proposed approach, the numerical results are compared with known exact solutions. The computations are carried out using various step sizes, and the findings demonstrate that the method provides highly accurate results. Enhanced accuracy is achieved by adopting sufficiently small step sizes. Furthermore, the numerical errors corresponding to different step sizes are thoroughly analyzed. Several examples are included to effectively demonstrate the accuracy and performance of the proposed finite difference method (FDM).

Keywords

• Finite difference method
• boundary value problem
• mathematical discretization
• convergence analysis

How to cite

Md. Amirul Islam, Nazmunnahar Naz, S. M. Kamal Hossain (2025). Numerical Investigation of Fourth-Order Boundary Value Problems Using the Finite Difference Method. Sonargaon University Journal, 5(I), 19–26.

@article{islam20258,
  title   = {Numerical Investigation of Fourth-Order Boundary Value Problems Using the Finite Difference Method},
  author  = {Md. Amirul Islam and Nazmunnahar Naz and S. M. Kamal Hossain},
  journal = {Sonargaon University Journal},
  volume  = {5},
  number  = {I},
  pages   = {19--26},
  year    = {2025},
  issn    = {2518-3125},
  url     = {https://su.edu.bd/journal/volume-5-issue-1/numerical-investigation-of-fourth-order-boundary-value-problems-using-the-finite}
}