Showing papers in "International Journal of Nonlinear Sciences and Numerical Simulation in 2021"

Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique

Abstract: Abstract In this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature.

Pandemic management by a spatio–temporal mathematical model

Abstract: Many researchers have tried to predict the impact of the COVID-19 outbreak on morbidity, in order to help policy-makers find optimal isolation policies. However, despite the development and use of many models and sophisticated tools, these forecasting attempts have largely failed. We present a model that considers the severity of the disease and the heterogeneity of contacts between the population in complex space–time dynamics. Using mathematical and computational methods, the applied tool was developed to analyze and manage the COVID-19 pandemic (from an epidemiological point of view), with a particular focus on population heterogeneity in terms of age, susceptibility, and symptom severity. We show improved strategies to prevent an epidemic outbreak. We evaluated the model in three countries, obtaining an average mean square error of 0.067 over a full month of the basic reproduction number (R0). The goal of this study is to create a theoretical framework for crisis management that integrates accumulated epidemiological considerations. An applied result is an open-source program for predicting the outcome of an isolation strategy for future researchers and developers who can use and extend our model. [ABSTRACT FROM AUTHOR] Copyright of International Journal of Nonlinear Sciences & Numerical Simulation is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Research on prediction model of thermal and moisture comfort of underwear based on principal component analysis and Genetic Algorithm–Back Propagation neural network

Abstract: Abstract In order to improve the efficiency and accuracy of thermal and moisture comfort prediction of underwear, a new prediction model is designed by using principal component analysis method to reduce the dimension of related variables and eliminate the multi-collinearity relationship between variables, and then inputting the converted variables into genetic algorithm (GA) and BP neural network. In order to avoid the problems of slow convergence speed and easy falling into local minimum of Back Propagation (BP) neural network, this paper adopted GA to optimize the weights and thresholds of BP neural network, and utilized MATLAB software to program, and established the prediction models of BP neural network and GA–BP neural network. To verify the superiority of the model, the predicted result of GA–BP, PCA–BP and BP are compared with GA–BP neural network. The results show that PCA could improve the accuracy and adaptability of GA–BP neural network for thermal and moisture comfort prediction. PCA–GA–BP model is obviously superior to GA–BP, PCA–BP, BP, SVM and K-means prediction models, which could accurately predict thermal and moisture comfort of underwear. The model has better accuracy prediction and simpler structure.

Noninstantaneous impulsive and nonlocal Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps

Abstract: Abstract In this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

Analysis of (α, β)-order coupled implicit Caputo fractional differential equations using topological degree method

Abstract: Abstract This article is devoted to establish the existence of solution of ( α , β ) $\\left(\\alpha ,\\beta \\right)$ -order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To support our main results, we present an example.

Nonlinear dynamics of a RLC series circuit modeled by a generalized Van der Pol oscillator

Abstract: Abstract In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system parameter are performed numerically through the fourth-order Runge–Kutta algorithm.

Wavelet-optimized compact finite difference method for convection–diffusion equations

Abstract: Abstract In this article, compact finite difference approximations for first and second derivatives on the non-uniform grid are discussed. The construction of diffusion wavelets using compact finite difference approximation is presented. Adaptive grids are obtained for non-smooth functions in one and two dimensions using diffusion wavelets. High-order accurate wavelet-optimized compact finite difference (WOCFD) method is developed to solve convection–diffusion equations in one and two dimensions on an adaptive grid. As an application in option pricing, the solution of Black–Scholes partial differential equation (PDE) for pricing barrier options is obtained using the proposed WOCFD method. Numerical illustrations are presented to explain the nature of adaptive grids for each case.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

Abstract: Abstract This paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

Numerical study of multi-dimensional hyperbolic telegraph equations arising in nuclear material science via an efficient local meshless method

Abstract: Abstract This research work is to study the numerical solution of three-dimensional second-order hyperbolic telegraph equations using an efficient local meshless method based on radial basis function (RBF). The model equations are used in nuclear material science and in the modeling of vibrations of structures. The explicit time integration technique is utilized to semi-discretize the model in the time direction whereas the space derivatives of the model are discretized by the proposed local meshless procedure based on multiquadric RBF. Numerical experiments are performed with the proposed numerical scheme for rectangular and non-rectangular computational domains. The proposed method solutions are converging quickly in comparison with the different existing numerical methods in the recent literature.

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract: Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β-derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β-derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Wavelet collocation methods for solving neutral delay differential equations

Abstract: In this paper we proposed wavelet based collocation methods for solving neutral delay differential equations. We use Legendre wavelet, Hermite wavelet, Chebyshev wavelet and Laguerre wavelet to solve the neutral delay differential equations numerically. We solve five linear and one nonlinear problem to demonstrate the accuracy of wavelet series solution. Wavelet series solution converges fast and gives more accurate results in comparison to other methods present in literature. We compare our results with Runge-Kutta-type methods by Wang et al. [1] and one-leg θ methods by Wang et al. [2] and observe that our results are more accurate.

A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

Abstract: Abstract In this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator

Abstract: In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the sufficient condition of commutators of p-adic fractional Hausdorff Operator by taking symbol function from Lipschitz space. Moreover, strong type estimates for fractional Hausdorff Operator and its commutator on weighted p-adic Lorentz space are also acquired.

Synchronization stability on the BAM neural networks with mixed time delays

Abstract: Abstract This article investigates the general decay synchronization (GDS) for the bidirectional associative memory neural networks (BAMNNs). Compared with previous research results, both time-varying delays and distributed time delays are taken into consideration. By using Lyapunov method and using useful inequality techniques, some sufficient conditions on the GDS for BAMNNs are derived. Finally, a numerical example is also carried out to validate the practicability and feasibility of our proposed results. It is worth pointing out that the GDS may be specialized as exponential synchronization, polynomial synchronization and logarithmic synchronization. Besides, we can estimate the convergence rate of the synchronization by GDS. The obtained results in this article can be seen as the improvement and extension of the previously known works.

A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint

Abstract: Abstract The slider-crank mechanism is used widely in modern industrial equipment whereby the contact-impact of a revolute clearance joint affects the dynamic behavior of mechanical systems. Combining multibody dynamic theory and nonlinear contact theory, the computational methodology for dynamic analysis of the slider-crank mechanism with a clearance joint is proposed. The differential equations of motion are obtained considering the revolute clearance joint between the connecting rod and slider. In the mechanical system, the contact force is evaluated using the continuous force model proposed by Lankarani and Nikravesh, which can describe the contact-impact phenomenon accurately. Then, the experimental study is performed whereby the numerical results are compared with the test data to validate the proposed model. Moreover, the dynamic response analysis is conducted with various driving velocities and clearance sizes, which also explains that the sensitive dependence of a mechanical system on the revolute clearance joint.

Exploring the effects of awareness and time delay in controlling malaria disease propagation

Abstract: Abstract In this article, a mathematical model has been derived for studying the dynamics of malaria disease and the influence of awareness-based interventions, for control of the same, that depend on ‘level of awareness’. We have assumed the disease transmission rates from vector to human and from human to vector, as decreasing functions of ‘level of awareness’. The effect of insecticides for controlling the mosquito population is influenced by the level of awareness, modelled using a saturated term. Organizing any awareness campaign takes time. Therefore a time delay has been incorporated in the model. Some basic mathematical properties such as nonnegativity and boundedness of solutions, feasibility and stability of equilibria have been analysed. The basic reproduction number is derived which depends on media coverage. We found two equilibria of the model namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable if basic reproduction number (ℛ0) is less than unity (ℛ0 < 1). Stability switches occur through Hopf bifurcation when time delay crosses a critical value. Numerical simulations confirm the main results. It has been established that awareness campaign in the form of using different control measures can lead to eradication of malaria.

Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control

Abstract: Abstract This paper is concerned about the impulsive control of a class of novel nonlinear fractional-order financial system with time-delay. Considering the variation of every states in the fractional-order financial system in the real world has certain delay for various reasons, thus we add corresponding delay on every state variable. Different from the traditional method of stability judgment, we choose two dimensions of time and space to analyze, which makes the process more accurate. In addition, the sufficient condition of the stability criterion for the fractional-order financial system based on impulsive control is derived. Moreover, the impulsive control can not only make the fractional-order financial system stable in different time delay but also in the different fractional operator. Consequently, the impulsive control has generality, universality and strong applicability. In the end, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed method.