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In the past few years, Haar wavelet-based numerical methods have been applied successfully to solve linear and nonlinear partial differential equations. This study aims to propose a wavelet collocation method based on Haar wavelets to identify a parameter in parabolic partial differential equations (PDEs). As Haar wavelet is defined in a very simple way, implementation of the Haar wavelet method becomes easier than the other numerical methods such as finite element method and spectral method. The computational time taken by this method is very less because Haar matrices and Haar integral matrices are stored once and used for each iteration. In the case of Haar wavelet method, Dirichlet boundary conditions are incorporated automatically. Apart from this property, Haar wavelets are compactly supported orthonormal functions. These properties lead to a huge reduction in the computational cost of the method.

The aim of this paper is to reconstruct the source control parameter arises in quasilinear parabolic partial differential equation using Haar wavelet-based numerical method. Haar wavelets possess various properties, for example, compact support, orthonormality and closed form expression. The main difficulty with the Haar wavelet is its discontinuity. Therefore, this paper cannot directly use the Haar wavelet to solve partial differential equations. To handle this difficulty, this paper represents the highest-order derivative in terms of Haar wavelet series and using successive integration this study obtains the required term appearing in the problem. Taylor series expansion is used to obtain the second-order partial derivatives at collocation points.

An efficient and accurate numerical method based on Haar wavelet has been proposed for parameter identification in quasilinear parabolic partial differential equations. Numerical results are obtained from the proposed method and compared with the existing results obtained from various finite difference methods including Saulyev method. It is shown that the proposed method is superior than the conventional finite difference methods including Saulyev method in terms of accuracy and CPU time. Convergence analysis is presented to show the accuracy of the proposed method. An efficient algorithm is proposed to find the wavelet coefficients at target time.

The outcome of the paper would have a valuable role in the scientific community for several reasons. In the current scenario, the parabolic inverse problem has emerged as very important problem because of its application in many diverse fields such as tomography, chemical diffusion, thermoelectricity and control theory. In this paper, higher-order derivative is represented in terms of Haar wavelet series. In other words, we represent the solution in multiscale framework. This would enable us to understand the solution at various resolution levels. In the case of Haar wavelet, this paper can achieve a very good accuracy at very less resolution levels, which ultimately leads to huge reduction in the computational cost.

Conventional isolated dc–dc converters offer an efficient solution for performing voltage conversion with a large improved voltage gain. However, the small-signal analysis of these converters shows that a right-half-plane (RHP) zero appears in their control-to-output transfer function, exhibiting a nonminimum-phase stability. This RHP zero can limit the frequency response and dynamic specifications of the converters; therefore, the output voltage response is sluggish. To overcome these problems, the purpose of this study is to analyze, model and design a new isolated forward single-ended primary-inductor converter (IFSEPIC) through RHP zero alleviation.

At first, the normal operation of the suggested IFSEPIC is studied. Then, its average model and control-to-output transfer function are derived. Based on the obtained model and Routh–Hurwitz criterion, the components are suitably designed for the proposed IFSEPIC, such that the derived dynamic model can eliminate the RHP zero.

The advantages of the proposed IFSEPIC can be summarized as: This converter can provide conditions to achieve fast dynamic behavior and minimum-phase stability, owing to the RHP zero cancellation; with respect to conventional isolated converters, a larger gain can be realized using the proposed topology; thus, it is possible to attain a smaller operating duty cycle; for conventional isolated converters, transformer core saturation is a major concern, owing to a large magnetizing current. However, the average value of the magnetizing current becomes zero for the proposed IFSEPIC, thereby avoiding core saturation, particularly at high frequencies; and the input current of the proposed converter is continuous, reducing input current ripple.

The key benefits of the proposed IFSEPIC are shown via comparisons. To validate the design method and theoretical findings, a practical implementation is presented.

Recently, the concept of the circular economy (CE) has witnessed significant momentum in academic and professional circles. However, there is a dearth of research that studies the enabling factors of the CE in the era of digital transformation. The existing research aimed to identify the impact of Industry 4.0 readiness on the CE in manufacturing firms operating in Jordan, as well as to identify the mediating role of the industrial Internet of things and big data analytics.

For this work objectives, 380 questionnaires were analyzed. Convergent validity and discriminant validity tests were performed through partial least squares-structural equation modelling (PLS-SEM) in the Smart-PLS programme. Data reliability was confirmed. A bootstrapping technique was used to analyze the data and then hypothesis testing was performed.

The results indicate that Industry 4.0 readiness, industrial Internet of things (IIoT) and big data analytics positively enable CE, also the IIoT and big data analytics positively mediate the nexus between Industry 4.0 readiness and CE.

This study promotes the idea of focusing on Industry 4.0 readiness to enhance CE in the Jordanian manufacturing sector and knowing the effect of IIoT and big data analytics in this relationship.

This research developed a theoretical model to understand how Industry 4.0 readiness might enhance the CE in manufacturing firms by invoking the IIoT and big data analytics as mediating constructs in the relationship between Industry 4.0 readiness and CE. This paper offers new theoretical and practical contributions that add value to industry 4.0 and CE literature by testing these constructs' mediation models in the manufacturing sector.