A hybrid reptile search algorithm and Levenberg-Marquardt algorithm based Haar wavelets to solve regular and singular boundary value problems

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F23%3A10253450" target="_blank" >RIV/61989100:27240/23:10253450 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s12597-023-00661-0" target="_blank" >https://link.springer.com/article/10.1007/s12597-023-00661-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s12597-023-00661-0" target="_blank" >10.1007/s12597-023-00661-0</a>

Result language

angličtina

Original language name

A hybrid reptile search algorithm and Levenberg-Marquardt algorithm based Haar wavelets to solve regular and singular boundary value problems

Original language description

Various engineering applications lead to the appearance of partial differential equations resulting in boundary value problems (BVPs). Orthogonal collocation method based Haar wavelets has gained significant attention in solving these problems. The Haar wavelets have several properties like vanishing moment, compact effect, and orthogonality. These properties prioritize being used as base functions for solving BVPs. However, the approximation leads to a relatively high number of unknown coefficients, which needs an efficient and reliable nonlinear solver to reach their values. The Levenberg-Marquardt algorithm (LM) is one of the most efficient nonlinear solvers. However, it may diverge in case of too far initial guesses, especially in many unknowns. The reptile search algorithm (RSA) is a recent reliable, nature-inspired optimization technique that has a noticeable capability in dealing with high-dimensional issues. Therefore, this paper proposes a hybrid optimization algorithm that integrates the RSA and LM algorithms using Haar wavelets as bases, named RSA-LM-Haar algorithm, to solve regular and singular natures of the BVPs more efficiently. To evaluate the performance of the proposed RSA-LM-Haar algorithm, it is tested on twelve case studies of BVPs including the singular and regular problems. The results are compared with those based on the LM alone, named LM-Haar algorithm. Finally, the applicability of the proposed algorithm is verified using two practical chemical applications to prove its ability to solve real-time applications effectively. All the results affirmed the capability of the proposed algorithm in solving both regular and singular BVPs. All results and comparisons illustrated that the proposed hybridization algorithm provides remarkable performance.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

OPSEARCH

ISSN

0030-3887

e-ISSN

0975-0320

Volume of the periodical

60

Issue of the periodical within the volume

4

Country of publishing house

IN - INDIA

Number of pages

31

Pages from-to

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UT code for WoS article

001016466100001

EID of the result in the Scopus database

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