The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential…
Abstract
Purpose
The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential transform method.
Design/methodology/approach
The paper considers two models of special interest in physics with fractional‐time derivative of order, namely, the time fractional mKdV equation and time fractional convection diffusion equation with nonlinear source term.
Findings
The numerical results demonstrate the significant features, efficiency and reliability of the proposed method and the effects of different values are shown graphically.
Originality/value
The paper shows that the results obtained from the fractional analysis appear to be general.
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Abdulhakim M. Masli, Musa Mangena, Ali Meftah Gerged and Donald Harradine
This study distinctively explores the firm-level and national-level determinants of audit committee effectiveness (ACE) in the Libyan banking sector (LBS).
Abstract
Purpose
This study distinctively explores the firm-level and national-level determinants of audit committee effectiveness (ACE) in the Libyan banking sector (LBS).
Design/methodology/approach
A mixed-methods approach has been employed to enhance the quality of the collected data and reduce the risk of bias. Five groups of actors in the Libyan banking sector were surveyed, including board members, AC members, executive managers, internal auditors and external auditors, further to interviewing a representative sample of these groups. In total, 218 survey responses were gathered, and 20 semi-structured interviews were conducted.
Findings
The study results show that AC authority, financial expertise and diligence are positively and significantly attributed to ACE, although AC independence and resources are not significantly related to ACE. The authors find that the legal and regulatory environment, government intervention, and the accounting and auditing environment are perceived as important and associated with ACE regarding national-level factors. These findings are strongly supported by semi-structured interviews and suggest that both firm-level and national-level factors are essential in understanding ACE in Libya's banking sector.
Research limitations/implications
The study’s evidence reiterates the vital need for more concentrated work to integrate governance, legislative and regulatory reforms to ensure the effectiveness of ACs as a key corporate governance (CG) mechanism in developing economies.
Originality/value
This study extends the literature relating measures of AC inputs and outputs by examining the perception of stakeholders to understand both the firm-level and national-level factors that affect ACE in a single institutional setting. Additionally, this work adds to the limited number of recent studies examining the role of ACs in the banking sector in developing economies.
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Z. F. Bhat, Sunil Kumar and Hina Fayaz Bhat
The aim of the article was to focus on various peptides identified in the egg and their probable application as novel ingredients in the development of functional food products…
Abstract
Purpose
The aim of the article was to focus on various peptides identified in the egg and their probable application as novel ingredients in the development of functional food products. Bioactive peptides of egg origin have attracted increasing interest as one of the prominent candidates for development of various health-promoting functional and designer foods.
Design/methodology/approach
Traditionally known as a source of highly valuable proteins in human nutrition, eggs are nowadays also considered as an important source of many bioactive peptides which may find wide application in medicine and food production. These specific protein fragments from egg proteins which, above and beyond their nutritional capabilities, have a positive impact on the body’s function or condition by affecting the digestive, endocrine, cardiovascular, immune and nervous systems, and may ultimately influence health.
Findings
Several peptides that are released in vitro or in vivo from egg proteins have been attributed to different health effects, including antihypertensive effects, antimicrobial properties, antioxidant activities, anticancer activity, immunomodulating activity, antiadhesive properties and enhancement of nutrient absorption and/or bioavailability. Extensive research has been undertaken to identify and characterize these biologically active peptides of egg origin which has changed the image of egg as a new source of biologically active ingredients for the development of functional foods with specific benefits for human health and treatment and prevention of diseases.
Originality/value
The paper mainly describes the above-stated properties of bioactive peptides derived from egg proteins.
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The purpose of this paper is to apply the variational iterations method to solve two difference types such as the modified Boussinesq (MB) and seven‐order Sawada‐Kotara (sSK…
Abstract
Purpose
The purpose of this paper is to apply the variational iterations method to solve two difference types such as the modified Boussinesq (MB) and seven‐order Sawada‐Kotara (sSK) equations and to compare this method with that obtained previously by Adomian decomposition.
Design/methodology/approach
The variational iteration method is used for finding the solution of the MB and sSK equations. The solution obtained is an infinite power series for appropriate initial condition. The numerical results obtain for nth approximation and compare with the known analytical solutions; the results show that an excellent approximation to the actual solution of the equations was achieved by using only three iterations.
Findings
The comparison demonstrates that the two obtained solutions are an excellent agreement. The numerical results calculated show that this method, variational iteration method, can be readily implemented to this type of nonlinear equation and excellent accuracy can be achieved. The results of variation iteration method confirm the correctness of those obtained by means of Adomian decomposition method.
Originality/value
The results presented in this paper show that the variational iteration method is a powerful mathematical tool for solving the MB and the sSK equations; it is also a promising method for solving other nonlinear equations.
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The purpose of this paper is to apply the exp‐function method to construct exact solutions of nonlinear wave equations. The proposed technique is tested on the (2+1) and (3+1…
Abstract
Purpose
The purpose of this paper is to apply the exp‐function method to construct exact solutions of nonlinear wave equations. The proposed technique is tested on the (2+1) and (3+1) dimensional extended shallow water wave equations. These equations play a very important role in mathematical physics and engineering sciences.
Design/methodology/approach
In this paper, the authors apply the exp‐function method to construct exact solutions of nonlinear wave equations.
Findings
In total, four forms of the extended shallow water wave equation have been studied, from the point of view of its exact solutions using computational method. Exp‐function method was employed to achieve the goal set for this work. The applied method will be used in further works to establish more entirely new solutions for other kinds of nonlinear wave equations. Finally, it is worthwhile to mention that the proposed method is straightforward, concise, and it is a promising and powerful new method for other nonlinear wave equations in mathematical physics.
Originality/value
The algorithm suggested in the paper is quite efficient and is practically well suited for use in these problems. The method is straightforward and concise, and its applications are promising.
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Sapna Pandit, Manoj Kumar, R.N. Mohapatra and Ali Saleh Alshomrani
This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.
Abstract
Purpose
This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.
Design/methodology/approach
First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.
Findings
Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.
Originality/value
The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.
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Mehdi Dehghan, Jalil Manafian Heris and Abbas Saadatmandi
The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.
Abstract
Purpose
The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.
Design/methodology/approach
This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.
Findings
This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.
Originality/value
The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.
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This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential…
Abstract
Purpose
This paper aims to propose an efficient and convenient numerical algorithm for two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations (of Hammerstein and mixed types).
Design/methodology/approach
The main idea of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic equations.
Findings
Without considering the integral operational matrix, this algorithm will adopt straightforward discrete data integral transformation, which can do good work to less computation and high precision. Besides, combining the convenient fractional differential operator of Bernoulli basis polynomials with the least-squares method, numerical solutions of the studied equations can be obtained quickly. Illustrative examples are given to show that the proposed technique has better precision than other numerical methods.
Originality/value
The proposed algorithm is efficient for the considered two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations. As its convenience, the computation of numerical solutions is time-saving and more accurate.
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Imtiyaz Ahmad Bhat, Lakshmi Narayan Mishra, Vishnu Narayan Mishra and Cemil Tunç
This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The…
Abstract
Purpose
This study focuses on investigating the numerical solution of second-kind nonlinear Volterra–Fredholm–Hammerstein integral equations (NVFHIEs) by discretization technique. The purpose of this paper is to develop an efficient and accurate method for solving NVFHIEs, which are crucial for modeling systems with memory and cumulative effects, integrating past and present influences with nonlinear interactions. They are widely applied in control theory, population dynamics and physics. These equations are essential for solving complex real-world problems.
Design/methodology/approach
Demonstrating the solution’s existence and uniqueness in the equation is accomplished by using the Picard iterative method as a key technique. Using the trapezoidal discretization method is the chosen approach for numerically approximating the solution, yielding a nonlinear system of algebraic equations. The trapezoidal method (TM) exhibits quadratic convergence to the solution, supported by the application of a discrete Grönwall inequality. A novel Grönwall inequality is introduced to demonstrate the convergence of the considered method. This approach enables a detailed analysis of the equation’s behavior and facilitates the development of a robust solution method.
Findings
The numerical results conclusively show that the proposed method is highly efficacious in solving NVFHIEs, significantly reducing computational effort. Numerical examples and comparisons underscore the method’s practicality, effectiveness and reliability, confirming its outstanding performance compared to the referenced method.
Originality/value
Unlike existing approaches that rely on a combination of methods to tackle different aspects of the complex problems, especially nonlinear integral equations, the current approach presents a significant single-method solution, providing a comprehensive approach to solving the entire problem. Furthermore, the present work introduces the first numerical approaches for the considered integral equation, which has not been previously explored in the existing literature. To the best of the authors’ knowledge, the work is the first to address this equation, providing a foundational contribution for future research and applications. This innovative strategy not only simplifies the computational process but also offers a more comprehensive understanding of the problem’s dynamics.