A high-order multi-resolution wavelet method for nonlinear systems of differential equations

Muhammad Ahsan, Weidong Lei, Martin Bohner and Amir Ali Khan

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 215, issue C, 543-559

Abstract: In this article, the applications of the new Haar wavelet collocation methods called as Haar wavelet collocation method (HWCM) and higher-order Haar wavelet collocation method (H-HWCM) are developed for the solution of linear and nonlinear systems of ordinary differential equations. The proposed H-HWCM is compared with a variety of other methods including the well-known HWCM. The quasi-linearization technique is introduced in the nonlinear cases. The stability and convergence of both techniques is studied in detail, which are the important parts to analyze the proposed methods. The efficiency of the methods is illustrated with certain numerical examples, but the H-HWCM is more accurate with faster convergence than the HWCM and other methods reported in the literature.

Keywords: Haar wavelet; H-HWCM; System of nonlinear differential equations; Collocation method; Quasi-linearization technique (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475423003683
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:215:y:2024:i:c:p:543-559

DOI: 10.1016/j.matcom.2023.08.032

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().