Advances and Applications in Discrete Mathematics

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DISCRETE LEAST SQUARE METHOD FOR SOLVING DIFFERENTIAL EQUATIONS

Authors

  • Salisu Ibrahim

Keywords:

discrete least square method (DLSM), $L_2$ norm, differential equations.

DOI:

https://doi.org/10.17654/0974165822021

Abstract

This paper investigates the least squares approach for finding approximate solutions to differential equations using discrete method. Our goal is to develop efficient numerical method (discrete method) for solving ordinary differential equations (ODEs). The  norm along with the discrete least squares method (DLSM) has been used  to obtain the least approximation error and numerical approximate solution, respectively. Some examples are given to support the explicit results.

Received: January 23, 2022
Accepted: March 28, 2022

References

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A. R. Firoozjaee and M. H. Afshar, Discrete least squares meshless method with sampling points for the solution of elliptic partial differential equations, Engineering Analysis with Boundary Elements 33(1) (2009), 83-92.

S. Ibrahim, Numerical approximation method for solving differential equations, Eurasian Journal of Science and Engineering 6(2) (2020), 157-168.

S. Ibrahim and A. Isah, Solving system of fractional order differential equations using Legendre operational matrix of derivatives, Eurasian Journal of Science and Engineering 7(1) (2021), 25-37.

S. Ibrahim and A. Rababah, Degree reduction of Bézier curves with Chebyshev weighted -continuity, Adv. Stud. Contemp. Math. 4(30) (2020), 471-476.

A. Isah and S. Ibrahim, Shifted Genocchi polynomial operational matrix for solving fractional order system, Eurasian Journal of Science and Engineering 7(1) (2021), 74-83.

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

A. Rababah and S. Ibrahim, Weighted -multi-degree reduction of Bézier curves, International Journal of Advanced Computer Science and Applications 7(2) (2016b), 540-545.

https://thesai.org/Publications/ViewPaper?Volume=7&Issue=2&Code=ijacsa &SerialNo=70.

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

A. Rababah and S. Ibrahim, Geometric degree reduction of Bézier curves, Springer Proceeding in Mathematics and Statistics, Book Chapter 8, 2018. https://www.springer.com/us/book/9789811320941.

S. Ibrahim and M. E. Koksal, Commutativity of sixth-order time-varying linear systems, Circuits, Systems, and Signal Processing 40(10) (2021), 4799-4832. https://doi.org/10.1007/s00034-021-01709-6.

Salisu Ibrahim, Commutativity of high-order linear time-varying systems, Advances in Differential Equations and Control Processes 27(1) (2022), 73-83. http://dx.doi.org/10.17654/0974324322013.

S. Ibrahim, Explicit commutativity and stability for the Heun’s linear time-varying differential systems, Authorea (2021).

https://doi.org/10.22541/au.162566323.35099726/v1

S. Ibrahim and M. E. Koksal, Realization of a fourth-order linear time-varying differential system with nonzero initial conditions by cascaded two second-order commutative pairs, Circuits, Systems, and Signal Processing 40(6) (2021), 3107-3123.

Salisu Ibrahim and Abedallah Rababah, Decomposition of fourth-order Euler-type linear time-varying differential system into cascaded two second-order Euler commutative pairs, Complexity 2022, Article ID 3690019, 9 pages. https://doi.org/10.1155/2022/3690019.

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Published

2022-08-07

Issue

Vol. 30 (2022)

Section

Articles

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How to Cite

DISCRETE LEAST SQUARE METHOD FOR SOLVING DIFFERENTIAL EQUATIONS. (2022). Advances and Applications in Discrete Mathematics, 30, 87-102. https://doi.org/10.17654/0974165822021

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