Functional and Matrix Approximation of Numerical Solution of Haar Wavelet

Authors

  • Oya Mert Department of Mathematics, Tekirdağ Namık Kemal University, Türkiye
  • Yasemin Bakır Management Information System, Fenerbahçe University, Türkiye

DOI:

https://doi.org/10.7546/CRABS.2024.06.01

Keywords:

collocation points, Haar wavelet method, numerical methods

Abstract

In this article, a uniform Haar wavelet approach is devised to numerically solve the differential equations. The uniform Haar wavelet coefficients are generated by employing collocation points. The generalized approach for function and matrix approximation using Haar wavelets is proposed. This study aims to decide which method is more useful by reflecting on the differences between the two methods. Also, the application of Haar wavelets to the solution of a first and second-order ODE is described in this research. To assess its applicability and efficiency, two test problems are used. The findings obtained are compared to those obtained using the function and matrix approximation methods. For numerically solving first and second-order ODEs, the Haar wavelet methodology gives a more reliable and exact method. By estimating error norms for various problems, the performance and accuracy of the method have been shown.

Author Biographies

Oya Mert, Department of Mathematics, Tekirdağ Namık Kemal University, Türkiye

Mailing Address:
Department of Mathematics,
Tekirdağ Namık Kemal University,
Tekirdağ
Türkiye

Email: oyamert@nku.edu.tr

Yasemin Bakır, Management Information System, Fenerbahçe University, Türkiye

Mailing Address:
Management Information System,
Fenerbahçe University
Istanbul
Türkiye

Email: yasemin.bakir@fbu.edu.tr

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Published

30-06-2024

How to Cite

[1]
O. Mert and Y. Bakır, “Functional and Matrix Approximation of Numerical Solution of Haar Wavelet”, C. R. Acad. Bulg. Sci. , vol. 77, no. 6, pp. 793–800, Jun. 2024.

Issue

Section

Mathematics