Wavelet Method Research Articles

A compact finite-difference and Haar wavelets collocation technique for parabolic volterra integro-differential equations

Abstract In this paper, a numerical investigation of a class of parabolic Volterra integro-differential equations (parabolic-VIDEs) is conducted. The approach focuses on semi-discretizing parabolic-VIDEs by utilizing a second-order compact finite difference method O ( δ t 2 ) for the time variable and approximating the integral term using the trapezoidal rule. Further, the spatial derivative is approximated by Haar wavelet method. This hybrid methodology leverages the strengths of both techniques to solve the equations more efficiently and accurately. The error analysis, using L 2 and L ∞-norms, shows low computational costs. Numerical experiments show that second-order accuracy in both time and space, respectively. Stability and convergence of the proposed method are given through Sobolve space. Some numerical examples are tested for the effectiveness and accuracy of the proposed method. Furthermore, the presented numerical approach is compared with standard finite difference numerical methods and the results are reported in a table.

A study for analysing predator–prey ecological system using Legendre polynomial

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on Caputo operators, we present a newly developed system of differential equations for the predator–prey system using wavelet method. It is well known that a system of nonlinear singular models cannot operate smoothly since they are singular and nonlinear. Therefore, with the help of this numerical approach, we have converted the system into a nonlinear system of algebraic equations by extending it through operational matrix of Legendre wavelets. Using the wavelet collocation scheme, we have calculated these unknown coefficients. It has been demonstrated in tables and graphs that the developed approach is consistent and proficient. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyse its behaviour. In addition, a nonlinear functional analysis have used to establish uniformly boundedness for the proposed model. Also we have discussed residual error analysis and Lyapunov exponent. The applicability and efficacy of this methodology have been demonstrated through this nonlinear system. Additionally, a comparison with existing results highlights the advantages of our numerical approach. All calculations have been done using MATLAB.

Choosing wavelet methods for otolith contour studies

Choosing wavelet methods for otolith contour studies

Geopolitical Risks and Stock Market Volatility in the SAARC Region

Abstract This study examined the stock market volatility of the member states of the South Asian Association for Regional Cooperation (SAARC) and geopolitical risk (GPR). The analysis period covered January 2014 to March 2024, and the time–frequency wavelet method was used to process the data. The time-varying parameter vector autoregression and spatial autoregressive models helped determine the dynamic connectedness of volatility in the analyzed states. The findings revealed similar stock market connections in Bangladesh and India. In addition, a comparative analysis of stocks in India and Pakistan led to the identification of common elements. The connection between geopolitical concerns and Sri Lankan stocks was the strongest and increased in intensity after 2019. GPR and Nepal’s stock market maintained a continuous but low-intensity relationship. The dynamic connectedness between member states’ stock markets was limited during the review period. The study results could encourage SAARC governments to bridge their political differences to ensure that South Asia becomes a strong partner in the global economy. Equally, our results can benefit investors, financial institutions, regulatory authorities, and governments.

Numerical solution based on the Haar wavelet collocation method for partial integro-differential equations of Volterra type

In this paper, a numerical investigation of a class of parabolic Volterra integro-differential equations has been carried out. Basically, the finite difference method associated with the Haar wavelet collocation technique is pursued. The main idea relies on semi-discretizing the parabolic-VIDEs by considering the finite differences in time and approximating the integral term within the trapezoidal rule. Afterwards, using a uniform mesh, the spatial derivative is approximated by the Haar wavelet method. Stability and convergence of the proposed approach are established in the frame of Sobolev space. Numerical examples are used to illustrate the effectiveness of this approach under different test scenarios. The error analysis, using both L 2 and L ∞ norms, shows that the method has high efficiency computationally with a great deal of accuracy. It is observed that these numerical results are in excellent agreement with the analytical solution. In addition, the methods and results obtained in this study are compared with those reported in recent literature.

The Effective Elastic Thickness of the Lithosphere Reveals Tectonic Process and Lithospheric Rheology of the Eurasian Basin

ABSTRACTWe obtained the effective elastic thickness of the lithosphere (Te) in the Eurasian Basin using the fan‐shaped wavelet method. For ultraslow spreading ridges, the magmatic heat input is insufficient to form continuous quasisteady‐state magma lenses along the axis, resulting in significant variability in the rheological strength of the lithosphere. We suggested that the tectonic inheritance resulted in the different lithospheric rheology of WVZ and SMZ, consequently leading to distinct tectonic‐magmatic activities. The SMZ with less magmatic activity has a weaker lithosphere than that of the EVZ with extensive magmatism. We propose that the lithospheric rheology and thermal structure of ultraslow spreading ridge may be influenced not by the amount of magma supply but by the mode of magma emplacement.

Carbon omission and financial market sustainability via government effectiveness: a cross-culture comparison of OECD and Asian emerging economies

PurposeFinancial market sustainability is gaining attention as investors and stakeholders become more aware of environmental, social and governance issues, pushing demand for responsible and ethical investment practices. Therefore, this study aims to investigate the impact of carbon (CO2) emissions from three sources, oil, gas and coal, on the stock market sustainability via effective government policies.Design/methodology/approachThe eight countries belong to two different regions of world: Asian economies such as Pakistan, India, Malaysia and China, and OECD economies such as Germany, France, the UK and the USA are selected as a sample of the study. The 22-year data from 2000 to 2022 are collected from the DataStream and the World Bank data portal for the specified countries. The generalized methods of movement (GMM) and wavelet are used as the econometric tool for the analysis.FindingsOur findings show that the CO2 emission from coal and gas significantly negatively impacts stock market sustainability, but CO2 emission from oil positively impacts stock market sustainability. Moreover, all the emerging Asian economies’ CO2 emissions from coal and gas have a much greater significant negative impact on the stock market sustainability than the OECD countries due to the critical situation. However, the government’s effective policies have a positive significant moderating impact between them, reducing the effect of CO2 emission on the stock market.Research limitations/implicationsThis study advocated strong implications for policymakers, governments and investors.Practical implicationsEffective government policies can protect the environment and make business operations suitable, leading to market financial stability. This study advocated strong implications for policymakers, governments and investors.Originality/valueThis study provides fresh evidence of the government’s effective role to control the carbon environment that provide the sustainability to the organizations with respect to OECD and emerging economy.

MHD Mixed Convection Boundary Layer Casson Nanofluid Flow over an Exponential Stretching Sheet

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

Highly Sensitive Electrochemical Detection of Chlorpromazine Using Broccoli‐Like Copper–Aluminum‐Layered Double Hydroxide‐Modified Platinum Electrode

AbstractChlorpromazine (CPZ), an antipsychotic drug derived from phenothiazine, can cause a range of adverse effects in humans, notably visual problems and hematological disorders upon consumption of chlorpromazine‐contaminated water. In this regard, a novel electrochemical sensing platform based on a copper–aluminum‐layered double hydroxide (Cu–Al LDH)‐modified platinum electrode for the highly sensitive and selective detection of chlorpromazine in groundwater samples has been developed. The immobilized Cu–Al LDH showed an electrocatalytic effect on chlorpromazine reduction and oxidation. Among the employed electroanalytical techniques, only the square‐wave voltammetry‐assisted Pt/Cu–Al LDH electrode could detect chlorpromazine with a remarkable sensitivity of 0.065 µA µM−1 over a broad linear detection range of 0.01–760 µM, with low detection and quantification limits of 4.86 and 16.18 nM, respectively. Furthermore, the developed electrode can rapidly detect chlorpromazine within less than 10 s. In addition, the diffusion profiles of steady‐state concentrations of oxidized and reduced chlorpromazine within the immobilized Cu–Al were studied using the Legendre wavelet method. Moreover, the developed Pt/Cu–Al LDH electrode demonstrated satisfactory rates in the quantification of chlorpromazine in groundwater samples, yielding satisfactory recovery rates (97.63–102.57%), confirming the practicability of the fabricated electrode in real‐time monitoring of chlorpromazine levels in groundwater without requiring any sample pretreatment.

Impact of rogue waves on semi-submersible platforms: An experimental investigation of wave run-up and air-gap responses

The wave run-up and air-gap responses of semi-submersible platforms under extreme sea conditions are crucial design considerations for ensuring the structural integrity and safety of marine engineering operations. This study investigated the impact of rogue waves on the wave run-up and air-gap responses of semi-submersible platforms using a transient focusing wave group to accurately simulate irregular seas. Comparative model tests were conducted on a semi-submersible platform under both rogue and non-rogue-wave conditions. The platform motions and air-gap responses were analysed using spectral analysis, extreme-value statistics, and wavelet methods. Rogue waves were found to significantly affect the air-gap response spectrum, increasing the nonlinearity of both the wave run-up and air-gap responses. Different locations on the platform exhibited varying statistical and spectral response characteristics. Rogue waves modified the instantaneous properties of wave elevation, thereby increasing the energy levels in the system. This study confirmed that rogue waves significantly influence the air-gap responses and wave run-up of semi-submersible platforms, suggesting that they should be considered when designing and planning the operations of these platforms. This study offers a comprehensive understanding of the complex interactions between rogue waves and large maritime structures and provides insights for improving safety and performance under extreme sea conditions.

Modified Hermite Wavelet Discrete Matrix Approach for the Brusselator Chemical Model

AbstractThe primary goal of this study is to create a wavelet collocation technique that can be used to solve nonlinear fractional order systems of ordinary differential equations, which are equations that arise in modeling problems related to auto‐catalytic chemical reactions. Using the Hermite wavelet collocation method (HWCM), the system of nonlinear ordinary differential equations of integer and fractional order is numerically solved. The nonlinear Brusselator system is transformed into an algebraic equation system using the collocation method and the fractional derivative operational matrices. The Newton‐Raphson method is used to solve these algebraic equations, and the approximate values of the derived unknown coefficients are substituted. Through the numerical examples, the method's computational effectiveness and correctness are illustrated with various model constraints. A numerical comparison is made between the current approach ND solver, RK method, and Haar wavelet method (HWM). The efficiency and reliability of the developed strategy's performance are shown in graphs and tables. The created Hermite wavelet collocation method is resilient and has good accuracy compared to current methods found in the literature. Numerical computations are performed through Mathematica, a mathematical software.

On computational analysis via fibonacci wavelet method for investigating some physical problems

On computational analysis via fibonacci wavelet method for investigating some physical problems

Improving solar HVAC performance by incorporating sutterby SiO2–Cu/C3H8O2 hybrid nanofluid flow via a collocation based Gegenbauer wavelets technique: Effects of electromagnetic control and Smoluchowksi's temperature slippage

AbstractThe utilization of solar energy in heating, ventilation, and air conditioning (HVAC) systems has gained significant attention as a sustainable and environmentally friendly solution to meet the increasing energy demands. Therefore, this research work introduces a novel engineering study that explores solar‐HVAC systems. However, the study utilized hybrid nanofluids (HNFs) consisting of silicon dioxide and copper nanoparticles, with propylene glycol serving as the base fluid. Furthermore, this exploration features a magnetohydrodynamics (MHD) driven rotating flow with activation energy to enhance the heat transfer performance of solar‐HVAC systems. To increase the model novelty, 3D mathematical models were developed to characterize boundary conditions, which include the speed slippery and Smoluchowski temperature slippage. The partial differential equations in the model are transformed into ordinary differential equations (ODEs) through the use of similarity transformations. The Wavelets and Gegenbauer wavelets method in Mathematica was utilized to solve ODEs and investigate physical attributes such as plate friction, Nusselt number, Sherwood number, and mass flux. The findings show that the solar thermal radiation and magnetic field improve the thermal transfer efficiency of solar‐HVAC. Therefore, the findings of the research have practical applications in solar energy for HVAC systems and can contribute to technological improvements in the manufacturing industry.

An Efficient Multi-Scale Wavelet Approach for Dehazing and Denoising Ultrasound Images Using Fractional-Order Filtering

Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an efficient multi-scale wavelet method for dehazing and denoising ultrasound images using a fractional-order filter, which integrates a guided filter, directional filter, fractional-order filter, and haze removal to the different resolution images generated by a multi-scale wavelet. In the directional filter stage, an eigen-analysis of each pixel is conducted to extract structural features, which are then classified into edges for targeted filtering. The guided filter subsequently reduces speckle noise in homogeneous anatomical regions. The fractional-order filter allows the algorithm to effectively denoise while improving edge definition, irrespective of the edge size. Haze removal can effectively eliminate the haze caused by attenuation. Our method achieved significant improvements, with PSNR reaching 31.25 and SSIM 0.905 on our ultrasound dataset, outperforming other methods. Additionally, on external datasets like McMaster and Kodak24, it achieved the highest PSNR (29.68, 28.62) and SSIM (0.858, 0.803). Clinical evaluations by four radiologists confirmed its superiority in liver and carotid artery images. Overall, our approach outperforms existing speckle reduction and structural preservation techniques, making it highly suitable for clinical ultrasound imaging.

Diagnosis of gas path health states on a real flight data by convolutional neural network and dual-tree complex wavelet

As the core component of aircraft, the reliability and availability of aero-engines directly affect the entire cruise process of aircraft. Implementing health monitoring in the gas path of an aero-engine can ensure engine reliability and availability to a greater extent. It can also enable the move from traditional time-scheduled maintenance to condition-based maintenance and reduce life cycle costs. The existing models were mainly concentrated on simulation data and traditional machine learning methods. This paper provides a new pathway to classify the states of engine gas path performance by combining the convolutional neural network (CNN) with the dual-tree complex wavelet (DTCW) method. A real flight data accompanied by maintenance records collected from the airline was adopted to construct a data set. The data pre-processing and stable points extraction were carried out, and the combined CNN and DTCW method was developed to diagnose the healthy states of the gas path. The final accuracy can achieve higher than 94%. The diagnosis results indicate that the deep learning methods hold particular promise for aero-engine health monitoring.

Bayesian continuous wavelet transform for time-varying damping identification of cables using full-field measurement

Cables serve as the primary load-bearing element in cable-stayed bridges, making their damping level critical for structural safety evaluation. Traditional operational modal analysis (OMA) faces challenges in damping identification due to result discreteness, and limited sensor deployment often leads to the loss of crucial modal information. This paper proposes a Bayesian continuous wavelet transform with Gabor wavelet (BCWT-G) method for time-varying damping identification using full-field measurement data. A computer vision technique combining the pyramid grafting network (PGNet) with neighboring frame pixel fitting (NFPF) is used to accurately capture full-field vibration data. The time-frequency domain properties of these data are then extracted and incorporated into a Bayesian probabilistic estimation framework for modal updating. The proposed method was validated through numerical simulations using a physics-based graphics model (PBGM), and actual cable testing under complex environments, demonstrating its effectiveness and robustness in identifying the time-varying dynamic characteristics of cables.

Combined failure identification of intermediate bearing in aeroengine based on wavelet transform, second-order difference, and 1D-LBP

Intermediate bearing is one of key parts in double-rotor aeroengine, whose running state usually can only be monitored by casing signals. As the fault characteristic information detected from casing is weak and complex, it is generally difficult to be dug correctly. One-dimensional local binary pattern (1D-LBP) can depict failure information from the perspective of local feature extraction. Currently, the study on the application of 1D-LBP in fault identification is mostly based on original signals; due to the influence of component signals irrelevant to fault and noise, the fault information in original signals is weak and complex; besides, 1D-LBP is rather sensitive to noise, which is extremely possible to cause insufficient extraction of local textural features and the difficulty to identify a fault. To solve this problem and make it possible to precisely identify the fault of intermediate bearing of real aeroengine, the paper has proposed the combined method of wavelet transform (WT), second-order difference with 1D-LBP. WT is highly uncertain to determine the decomposition layer number. To solve the difficulty, correlation coefficient was introduced. Meanwhile, casing vibration signal was subjected to WT. Furthermore, because vibration signal often went with impact components in a bearing failure and second-order difference of signals was sensitive to impact feature, component signals obtained by WT were subjected to second-order difference operation. Additionally, taking advantage of 1D-LBP, second-order differences of signals were locally binarized with average value as criterion. Finally, 1D-LBP signals were re-transformed to decimal 1D local texture signals (1D-LTS). These 1D-LTS can embody local feature information of signals. According to the spectrum of 1D-LTS, combined failure type of intermediate bearing was identified. Through the comparison with WT and classical 1D-LBP method, and failure analysis after disassembly of aeroengine, the effectiveness and engineering applicability of proposed method have been verified.

Thermohaline convection in MHD Casson fluid over an exponentially stretching sheet

Abstract This study investigates the thermohaline convection in MHD Casson fluid over an exponentially stretching sheet. This study has practical significance in industrial processes, materials processing, energy systems, and environmental applications. The governing equations describing the conservation for an electrically conducting fluid flow, thermal and concentration transports are considered based on the principles of mass, momentum, energy and concentration equations. Our first step involves transforming the governing nonlinear partial differential equations into a coupled nonlinear ordinary differential equations with the help of suitable similarity transformations. Second step, infinite domain [0, ∞) of the problem to a finite domain [0, 1] through a coordinate transformations. This specific choice is motivated by the wavelet's significance in the finite domain of [0, 1]. Third step, we effectively solve the resulting coupled nonlinear ordinary differential equations using the numerical Hermite wavelet method (HWM). This approach proves to be a valuable technique for obtaining significant results and insights in our study. Finally, the effect of known physical parameters on velocity, temperature and concentration are analysed through tables and graphs.

Characterizing the local and global climatic factors associated with vegetation dynamics in the karst region of southwest China

Understanding the relationship between vegetation and climatic drivers is essential for assessing terrestrial ecosystem patterns and managing future vegetation dynamics. This study examines the effects of local climatic factors and remote large-scale ocean–atmosphere circulations from the Pacific, Atlantic, and Arctic Oceans, as well as the East Asian and Indian summer monsoons, on the spatiotemporal variability of the Normalized Difference Vegetation Index (NDVI) in the karst region of southwest China (KRSC) using Mann-Kendall test, Sen’s slope, cross-correlation, and wavelet analysis. We observed a significant increase in NDVI over karst and non-karst regions from 1981 to 2019, with a notable abrupt shift from 2001 onwards, underscoring the importance of understanding the underlying drivers. The significant correlation and coherence of surface air (TMP) and soil temperatures (ST) with NDVI, especially when analyzed using wavelet methods, indicate their crucial role in vegetation dynamics. Additionally, the broad coherence patterns of AMO and WHWP with NDVI at annual and decadal cycles suggest that ocean–atmosphere interactions also play a significant part. At interannual periodicities, most large-scale indices displayed significant coherence with NDVI. These findings highlight the complexity of NDVI variability, which is better explained by the integration of multiple local and global factors rather than by single variables. The integrated local–global drivers, particularly TMP-ST-AMO-NP-WHWP and PCP-SM-AMO-NP-WHWP with mean coherence of 0.90 and 0.89, respectively, showed the highest mean coherence, emphasizing the need for a multifaceted approach in understanding vegetation changes rather than a single local variable or atmospheric circulation index. These findings have significant implications for policymakers, aiding in better planning and policy formulations considering climate change and atmospheric variability.

Numerical study of hybrid nanofluid and thermal transport in sun-powered energy ship within the application of parabolic trough solar collectors

PurposeRecent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation.Design/methodology/approachThe mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome.FindingsThe velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs).Practical implicationsAdditionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry.Originality/valueThe originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers.