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Rachman, Alifira Meliana
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Computer Science & IT Education Mathematics Other

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Comparison Study between Shooting and Finite Difference Methods for Solving Linear Boundary Value Problem with Dirichlet, Neumann, and Robin Boundary Conditions Ardiana, Dita; Rachman, Alifira Meliana; Nurkarimah, Dwi; Habibah, Ummu
Indonesian Journal of Mathematics and Applications Vol. 3 No. 1 (2025): Indonesian Journal of Mathematics and Applications (IJMA)
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2025.003.01.2

Abstract

This study conducts a comparative analysis of the Shooting and Finite Difference methods for solving boundary value problems (BVPs) in ordinary differential equations (ODEs). The findings indicate that the Shooting method offers superior accuracy, particularly for smaller step sizes, whereas the Finite Difference method is more straightforward to implement and exhibits greater computational efficiency. The results further demonstrate that the Shooting method is particularly highly appropriate for problems with Dirichlet boundary conditions, as it achieves the lowest mean absolute error (MAE) across various step sizes. Conversely, the Finite Difference method attains higher computational efficiency for the same problem type but performs less advantageously in cases involving other boundary conditions. In contrast, the Shooting method demonstrates greater efficiency in solving problems with Neumann and Robin boundary conditions. The selection of an appropriate numerical method depends on the specific characteristics of the problem, necessitating a balance between accuracy and computational cost. This study provides a comprehensive evaluation of these numerical approaches to support the selection of the most suitable method for efficiently and accurately solving BVPs.
Comparison Study between Shooting and Finite Difference Methods for Solving Linear Boundary Value Problem with Dirichlet, Neumann, and Robin Boundary Conditions Ardiana, Dita; Rachman, Alifira Meliana; Nurkarimah, Dwi; Habibah, Ummu
Indonesian Journal of Mathematics and Applications Vol. 3 No. 1 (2025): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2025.003.01.2

Abstract

This study conducts a comparative analysis of the Shooting and Finite Difference methods for solving boundary value problems (BVPs) in ordinary differential equations (ODEs). The findings indicate that the Shooting method offers superior accuracy, particularly for smaller step sizes, whereas the Finite Difference method is more straightforward to implement and exhibits greater computational efficiency. The results further demonstrate that the Shooting method is particularly highly appropriate for problems with Dirichlet boundary conditions, as it achieves the lowest mean absolute error (MAE) across various step sizes. Conversely, the Finite Difference method attains higher computational efficiency for the same problem type but performs less advantageously in cases involving other boundary conditions. In contrast, the Shooting method demonstrates greater efficiency in solving problems with Neumann and Robin boundary conditions. The selection of an appropriate numerical method depends on the specific characteristics of the problem, necessitating a balance between accuracy and computational cost. This study provides a comprehensive evaluation of these numerical approaches to support the selection of the most suitable method for efficiently and accurately solving BVPs.
Co-Authors Ardiana, Dita Nurkarimah, Dwi Ummu Habibah, Ummu