Numerical Approximation Method for Solving Differential Equations

Authors

  • Salisu Ibrahim Department of Mathematics Education, Faculty of Education, Tishk International University, Erbil, Iraq

DOI:

https://doi.org/10.23918/eajse.v6i2p157

Keywords:

The Least Square Method (LSM), Ordinary Differential Equations, L_2 Norm

Abstract

This paper investigates numerical methods for solving differential equation. In this work, the continuous least square method (CLSM) was considered to find the best numerical approximation by solving differential equations. The continuous least square method (CLSM) was developed together with the L_2 norm. Numerical results obtained yield minimum approximation error, provide the best approximation. Explicit results obtained are supported by examples treated with MATLAB and Wolfram Mathematica 11.

References

Eason, E. D. (1976). A review of least square method for solving differential equation. International Journal for Numerical Method in Engineering, 10, 1021-1046.

Ibrahim, S., & Rababah, A. (2020). Degree reduction of Bézier curves with Chebyshev weighted G^3-continuity, Advanced studies in Contemporary Mathematics, 4(30), 471 – 476.

Katayoun, B. k. (2004). Solving differential equations with least square and collocation methods. Master of Science in Engineering Management George Washington University.

Loghmani, G. B. (2008). Application of least square method to arbitrary-order problems with separated boundary condition. Journal of computational and Applied Mathematics, 222, 500-510.

Rababah, A., & Ibrahim, S. (2016a). Weighted G^0- and G^1- multi-degree reduction of Bézier curves. AIP Conference Proceedings, 7 (2), 1738 -1742. https://doi.org/10.1063/1.4951820.

Rababah, A., & Ibrahim, S. (2016b). Weighted G^1-multi-degree reduction of Bézier curves. International Journal of Advanced Computer Science and Applications, 7(2), 540-545. Retrieved from https://thesai.org/Publications/ViewPaper?Volume=7&Issue=2&Code=ijacsa&SerialNo=70

Rababah, A., & Ibrahim, S. (2016c). Weighted degree reduction of Bézier curves with G^2-continuity. International Journal of Advanced and Applied Science, 3(3),13-18.

Rababah, A., & Ibrahim, S. (2018). Geometric degree reduction of Bézier curves. Springer Proceeding in Mathematics and Statistics. Retrieved from https://springer.com/us/book/9789811320941

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Published

2020-12-29

Issue

Section

Articles

How to Cite

Ibrahim, S. (2020). Numerical Approximation Method for Solving Differential Equations. EURASIAN JOURNAL OF SCIENCE AND ENGINEERING, 6(2), 157-168. https://doi.org/10.23918/eajse.v6i2p157

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