An Overview of Iweobodo-Mamadu-Njoseh Wavelet (IMNW) and Its Steps in Solving Time Fractional Advection-Diffusion Problems

D. C, Iweobodo; I. N, Njoseh; J. S., Apanapudor

doi:10.9734/arjom/2024/v20i3791

ARJOM

2024

DOI: 10.9734/arjom/2024/v20i3791

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An Overview of Iweobodo-Mamadu-Njoseh Wavelet (IMNW) and Its Steps in Solving Time Fractional Advection-Diffusion Problems

Iweobodo D. C,

Njoseh I. N,

Apanapudor J. S.

Abstract: This paper revisited the newly constructed wavelet-based Galerkin finite element technique by Iweobodo et al (2023) and reiterated the steps in seeking approximate solutions to time-fractional advection -diffusion problems with the method. Orthogonal polynomials, Mamadu-Njoseh polynomials and finite element method were discussed in relation to Iweobodo-Mamadu-Njoseh wavelet (IMNW) and the step-by-step application of the wavelet-based Galerkin finite element technique using the (IMNW) as a basis function was it… Show more

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Cited by 3 publications

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A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

Iweobodo,

Abanum,

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et al. 2024

Partial Differential Equations in Applied Mathematics

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A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

Iweobodo,

Abanum,

Ochonogor

et al. 2024

Partial Differential Equations in Applied Mathematics

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It can be difficult to optimize complex issues, and doing so frequently calls for the application of cutting-edge methods like mathematical modelling and evolutionary algorithms. Our proposal in this work is to address complex optimization issues using a hybrid strategy that integrates both approaches. The suggested method builds a surrogate model of the issue by mathematical modelling, which is subsequently optimized through the application of evolutionary algorithms. The hybrid methodology is tested against other optimization methods, such as particle swarm optimization and genetic algorithms, on a series of benchmark tasks. The experimental findings demonstrate that in terms of both computing time and solution quality, the suggested hybrid strategy performs better than various alternative methods. The suggested methodology exhibits great potential as a means of resolving intricate optimization issues across diverse fields, such as engineering, finance, and healthcare.

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Integrating Artificial Intelligence and Mathematical Models for Predictive Maintenance in Industrial Systems

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Predictive maintenance is a critical task for ensuring the reliability and efficiency of industrial systems. The integration of artificial intelligence (AI) and mathematical models has shown great potential in improving the accuracy and efficiency of predictive maintenance. This study provides an overview of the different types of mathematical models used for predictive maintenance, including physics-based, data-driven, and hybrid models. The study also discusses how AI techniques, such as machine learning and deep learning, can be used to enhance the accuracy and efficiency of predictive maintenance models. Additionally, the article highlights some of the challenges and limitations of integrating AI and mathematical models for predictive maintenance in industrial systems. Finally, this study provides a case study to demonstrate the practical application of the integrated approach for predictive maintenance in an industrial setting. This article aims to provide a comprehensive overview of the state-of-the-art in integrating AI and mathematical models for predictive maintenance and to provide guidance for researchers and practitioners working in this field.

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An Overview of Iweobodo-Mamadu-Njoseh Wavelet (IMNW) and Its Steps in Solving Time Fractional Advection-Diffusion Problems

Cited by 3 publications

References 16 publications

A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

A Hybrid Approach to Solving Complex Optimization Problems Using Evolutionary Algorithms and Mathematical Modeling

Integrating Artificial Intelligence and Mathematical Models for Predictive Maintenance in Industrial Systems

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