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1 – 10 of 25Mostafa Abbaszadeh, AliReza Bagheri Salec and Shurooq Kamel Abd Al-Khafaji
The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is…
Abstract
Purpose
The space fractional PDEs (SFPDEs) play an important role in the fractional calculus field. Proposing a high-order, stable and flexible numerical procedure for solving SFPDEs is the main aim of most researchers. This paper devotes to developing a novel spectral algorithm to solve the FitzHugh–Nagumo models with space fractional derivatives.
Design/methodology/approach
The fractional derivative is defined based upon the Riesz derivative. First, a second-order finite difference formulation is used to approximate the time derivative. Then, the Jacobi spectral collocation method is employed to discrete the spatial variables. On the other hand, authors assume that the approximate solution is a linear combination of special polynomials which are obtained from the Jacobi polynomials, and also there exists Riesz fractional derivative based on the Jacobi polynomials. Also, a reduced order plan, such as proper orthogonal decomposition (POD) method, has been utilized.
Findings
A fast high-order numerical method to decrease the elapsed CPU time has been constructed for solving systems of space fractional PDEs.
Originality/value
The spectral collocation method is combined with the POD idea to solve the system of space-fractional PDEs. The numerical results are acceptable and efficient for the main mathematical model.
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Bahram Jalili, Milad Sadinezhad Fard, Yasir Khan, Payam Jalili and D.D. Ganji
The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet…
Abstract
Purpose
The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.
Design/methodology/approach
The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.
Findings
The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.
Originality/value
Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.
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Imtiyaz Ahmad Bhat, Lakshmi Narayan Mishra, Vishnu Narayan Mishra, Cemil Tunç and Osman Tunç
This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in…
Abstract
Purpose
This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.
Design/methodology/approach
The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.
Findings
Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.
Research limitations/implications
The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.
Practical implications
There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.
Social implications
This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.
Originality/value
To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.
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Zuanbo Zhou, Wenxin Yu, Junnian Wang, Yanming Zhao and Meiting Liu
With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional…
Abstract
Purpose
With the development of integrated circuit and communication technology, digital secure communication has become a research hotspot. This paper aims to design a five-dimensional fractional-order chaotic secure communication circuit with sliding mode synchronous based on microcontroller (MCU).
Design/methodology/approach
First, a five-dimensional fractional-order chaotic system for encryption is constructed. The approximate numerical solution of fractional-order chaotic system is calculated by Adomian decomposition method, and the phase diagram is obtained. Then, combined with the complexity and 0–1 test algorithm, the parameters of fractional-order chaotic system for encryption are selected. In addition, a sliding mode controller based on the new reaching law is constructed, and its stability is proved. The chaotic system can be synchronized in a short time by using sliding mode control synchronization.
Findings
The electronic circuit is implemented to verify the feasibility and effectiveness of the designed scheme.
Originality/value
It is feasible to realize fractional-order chaotic secure communication using MCU, and further reducing the synchronization error is the focus of future work.
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Ran Wang, Yunbao Xu and Qinwen Yang
This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.
Abstract
Purpose
This paper intends to construct a new adaptive grey seasonal model (AGSM) to promote the application of the grey forecasting model in quarterly GDP.
Design/methodology/approach
Firstly, this paper constructs a new accumulation operation that embodies the new information priority by using a hyperparameter. Then, a new AGSM is constructed by using a new grey action quantity, nonlinear Bernoulli operator, discretization operation, moving average trend elimination method and the proposed new accumulation operation. Subsequently, the marine predators algorithm is used to quickly obtain the hyperparameters used to build the AGSM. Finally, comparative analysis experiments and ablation experiments based on China's quarterly GDP confirm the validity of the proposed model.
Findings
AGSM can be degraded to some classical grey prediction models by replacing its own structural parameters. The proposed accumulation operation satisfies the new information priority rule. In the comparative analysis experiments, AGSM shows better prediction performance than other competitive algorithms, and the proposed accumulation operation is also better than the existing accumulation operations. Ablation experiments show that each component in the AGSM is effective in enhancing the predictive performance of the model.
Originality/value
A new AGSM with new information priority accumulation operation is proposed.
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Maryam Mohseni and Davood Rostamy
The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present…
Abstract
Purpose
The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present the biorthogonal flatlet multiwavelet collocation method (BFMCM) as a numerical scheme for a class of system of Lane–Emden equations with initial or boundary or four-point boundary conditions.
Design/methodology/approach
The approach is involved in combining the biorthogonal flatlet multiwavelet (BFM) with the collocation method. The authors investigate the properties and procedure of the BFMCM for first time on this class of equations. By using the BFM and the collocation points, the method is constructed and it transforms the nonlinear differential equations problem into a system of nonlinear algebraic equations. The unknown coefficients of the assuming solution are determined by solving the obtained system. Additionally, convergence analysis and numerical stability of the suggested method are provided.
Findings
According to the attained results, the proposed BFMCM has more accurate results in comparison with results of other methods. The maximum absolute errors are calculated by using the BFMCM for comparison purposes provided.
Originality/value
The key desirable properties of BFMCM are its efficiency, simple applicability and minimizes errors. Therefore, the proposed method can be used to solve nonlinear problems or problems with singular points.
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This study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.
Abstract
Purpose
This study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.
Design/methodology/approach
The parabolic AD equations are reduced to the nonhomogeneous elliptic system of partial differential equations by utilizing the Chebyshev spectral collocation method (ChSCM) in the temporal variable. The implicit-explicit local differential transform method (IELDTM) is constructed over two- and three-dimensional meshes using continuity equations of the neighbor representations with either explicit or implicit forms in related directions. The IELDTM yields an overdetermined or underdetermined system of algebraic equations solved in the least square sense.
Findings
The IELDTM has proven to have excellent convergence properties by experimentally illustrating both h-refinement and p-refinement outcomes. A distinctive feature of the IELDTM over the existing numerical techniques is optimizing the local spatial degrees of freedom. It has been proven that the IELDTM provides more accurate results with far fewer degrees of freedom than the finite difference, finite element and spectral methods.
Originality/value
This study shows the derivation, applicability and performance of the IELDTM for solving 2D and 3D advection-diffusion equations. It has been demonstrated that the IELDTM can be a competitive numerical method for addressing high-space dimensional-parabolic partial differential equations (PDEs) arising in various fields of science and engineering. The novel ChSCM-IELDTM hybridization has been proven to have distinct advantages, such as continuous utilization of time integration and optimized formulation of spatial approximations. Furthermore, the novel ChSCM-IELDTM hybridization can be adapted to address various other types of PDEs by modifying the theoretical derivation accordingly.
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The main goal of this paper is to investigate whether there is long-memory behavior in the CBOE Brazil ETF volatility index (named here VIXBR). As structural breaks may create a…
Abstract
Purpose
The main goal of this paper is to investigate whether there is long-memory behavior in the CBOE Brazil ETF volatility index (named here VIXBR). As structural breaks may create a spurious long-range dependence, the presence of structural breaks is also gauged.
Design/methodology/approach
The study considers the period from October 2011 to March 2021, using daily data. To test the long-memory behavior, three empirical approaches are adopted: GPH, ELW and robust GPH (RGPH) estimator. To estimate the structural break points adopted to date the subsamples, the ICSS algorithm is used.
Findings
Results considering the total period (TP) and subsamples show that the breaks did not create a spurious long-memory behavior and together with the rolling estimation, reveal strong evidence of the long-range dependence in the CBOE Brazil ETF volatility index. The higher degree of persistent of the VIXBR series suggests an extended period of increased uncertainty that agents need consider when making their investment decision.
Research limitations/implications
As possible extension of this study is to investigate the behavior of long memory and structural breaks for different frequencies (weekly, monthly, among others).
Practical implications
The presence of long-range dependence in the CBOE Brazil ETF volatility index reveals that the past information is important for the predictability of risks, and therefore, can help to protect against market risks, which has important implications regarding the future decisions of economic agents (for example, policy makers and investors).
Originality/value
Brazil is an emerging capital market (ECM) that has attracted a great deal of attention from investors and investment funds seeking to diversify its assets. This paper contributes to the empirical financial literature, by studying the long-memory behavior of the CBOE Brazil ETF volatility index, considering possible structural breaks. To the best of knowledge, this has not been done so far.
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Feifei Zhong, Guoping Liu, Zhenyu Lu, Lingyan Hu, Yangyang Han, Yusong Xiao and Xinrui Zhang
Robotic arms’ interactions with the external environment are growing more intricate, demanding higher control precision. This study aims to enhance control precision by…
Abstract
Purpose
Robotic arms’ interactions with the external environment are growing more intricate, demanding higher control precision. This study aims to enhance control precision by establishing a dynamic model through the identification of the dynamic parameters of a self-designed robotic arm.
Design/methodology/approach
This study proposes an improved particle swarm optimization (IPSO) method for parameter identification, which comprehensively improves particle initialization diversity, dynamic adjustment of inertia weight, dynamic adjustment of local and global learning factors and global search capabilities. To reduce the number of particles and improve identification accuracy, a step-by-step dynamic parameter identification method was also proposed. Simultaneously, to fully unleash the dynamic characteristics of a robotic arm, and satisfy boundary conditions, a combination of high-order differentiable natural exponential functions and traditional Fourier series is used to develop an excitation trajectory. Finally, an arbitrary verification trajectory was planned using the IPSO to verify the accuracy of the dynamical parameter identification.
Findings
Experiments conducted on a self-designed robotic arm validate the proposed parameter identification method. By comparing it with IPSO1, IPSO2, IPSOd and least-square algorithms using the criteria of torque error and root mean square for each joint, the superiority of the IPSO algorithm in parameter identification becomes evident. In this case, the dynamic parameter results of each link are significantly improved.
Originality/value
A new parameter identification model was proposed and validated. Based on the experimental results, the stability of the identification results was improved, providing more accurate parameter identification for further applications.
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Priyaranjan Biswal and Prases Kumar Mohanty
Legged walking robots have numerous advantages over the wheel or tracked robots due to their strong operational ability and exposure to the complex environment. This paper aims to…
Abstract
Purpose
Legged walking robots have numerous advantages over the wheel or tracked robots due to their strong operational ability and exposure to the complex environment. This paper aims to present details about the mechanical formation and a new conceptual elliptical trajectory generation discussed throughout the paper of the quadruped robot.
Design/methodology/approach
Initially, a realistic CAD model of the four-legged robot is developed in Solidwork-2019. The proposed model’s forward and inverse kinematics equations are deduced using Denavit–Hartenberg parameters. Based on geometry and kinematics, manipulability and obstacle avoidance are investigated. A method of galloping trajectory is proposed for aiming the increase of upright direction impulse, which is produced by ground reaction force at each step frequency. Furthermore, the locomotion equation of the ellipse trajectory is derived by setting transition angle polynomial of free-fall phase, stance phase and swing phase and the constraints.
Findings
Finally, a successive simulation on a 2D sagittal plane is performed to check and verify the usefulness of the proposed trajectory. Before the development of the full quadruped, a single prototype leg is generated for experimental verification of the dynamic simulations.
Originality/value
The proposed trajectory is novel in that it uses force tracking control, which is intended to improve the quadruped robot’s robustness and stability.
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