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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Efficient design of neural network based on modified LM training algorithm for solving nonlinear 4th order 3D-PDEs 

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pp. 225–234Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2012XML
Received:
05 Mar 2025
Published Online:
29 Jan 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2012
Pages:
225–234

Abstract

Authors in this work design efficient neural networks, which are based on the modified Levenberg - Marquardt (LM) training algorithms to solve non-linear fourth - order three -dimensional partial differential equations in the two kinds in the periodic and in the non-periodic - Periodic. Software reliability growth models are essential tools for monitoring and evaluating the evolution of software reliability. Software defect detection events that occur during testing and operation are often treated as counting processes in many current models. However, when working with large software systems, the error detection process should be viewed as a random process with a continuous state space, since the number of faults found during testing is vast and the number of faults corrected by bug fixing changes only insignificantly. The suggested design addressing minimization problems employs a feed-forward approach to solve problems like these equations by converting the original problem into an optimization. Efficient design is achieved through a calculated parameter for learning with high precision. To clarify applicability, reliability, and accuracy for this design, some examples are provided. Additionally, to demonstrate the efficiency of the proposed design, comparisons were conducted with other designs.

Keywords

Subject Classifications

Primary 93A30Secondary 49K15

References

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