Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method by Mohammed Hamaidi, Ahmed Naji, Ahmed Taik

“…The advantages of such formulation are (i) time discretization as implicit, explicit, θ-method, method-of-line approach, and others are not applied; (ii) the time stability analysis is not discussed; and (iii) recomputation of the resulting matrix at each time level as done for other methods for solving partial differential equations (PDEs) with variable coefficients is avoided and the matrix is computed once. …”
Get full text

Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis by Firaol Asfaw Wodajo, Temesgen Tibebu Mekonnen

“…The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. …”
Get full text

The levelized cost of energy in the presence of uncertainty on the offshore wind speed by J. Pablo Arenas-López, Mohamed Badaoui

“…To carry out this task, we employ two techniques based on stochastic differential equations to generate wind power scenarios. Utilizing 40 years of recorded wind speed data sourced from the MERRA-2 reanalysis, we derive the input parameters of the models from fitting to 4-parameter Dagum and Johnson SB probability distributions, which shows that accurate modeling of offshore wind speeds requires dealing with complex mathematical functions that need numerical computation. …”
Get full text

Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions by Akhtar Hussain, Tarek F. Ibrahim, F. M. Osman Birkea, Abeer M. Alotaibi, Bushra R. Al-Sinan, Herbert Mukalazi

“…Abstract Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. …”
Get full text

New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
Get full text

Motion Control of a 4WS4WD Path-Following Vehicle: Dynamics-Based Steering and Driving Models by Zhonghua Zhang, Caijin Yang, Weihua Zhang, Yanhai Xu, Yiqiang Peng, Maoru Chi

“…The vehicle path-following dynamics are modeled using the classical mass-damper-spring vibration theory, which is described by three ordinary differential equations of second order with lateral, heading and velocity deviations, and control parameters. …”
Get full text

Positive Solutions Depending on Parameters for a Nonlinear Fractional System with p-Laplacian Operators by Chen Yang, Xiaolin Zhu

“…This paper considers a system of fractional differential equations involving p-Laplacian operators and two parameters D0+α1φp1D0+β1ut+λft,ut,vt=0,0<t<1,D0+α2φp2D0+β2vt+μgt,ut,vt=0,0<t<1,u0=u1=u′0=u′1=0,D0+β1u0=0,D0+β1u1=b1D0+β1uη1,v0=v1=v′0=v′1=0,D0+β2v0=0,D0+β2v1=b2D0+β2vη2, where αi∈1,2, βi∈3,4, D0+αi and D0+βi are the standard Riemann-Liouville derivatives, φpis=spi−2s,pi>1, φpi−1=φqi, 1/pi+1/qi=1,ηi∈0,1,bi∈0,ηi1−αi/pi−1, i=1,2, and f,g∈C0,1×0,+∞×0,+∞,0,+∞ and λ and μ are two positive parameters. …”
Get full text

Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. …”
Get full text

The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate by Kustarev G.V., Pavlov S.A., Rusinov K.A., Gusev A.A., Novotortsev N.V.

“…The integral differential equations determining the embedding of a rigid body of finite dimensions are solved using the discretization approach. …”
Get full text

Exploring the implications of ternary Jeffrey nanofluid on pulsating flow and heat transfer through unsymmetrical corrugated micro conduit by Mohamed S. Abdel-wahed, Khaled S. Mekheimer, Ahmed Y. Sayed, Shaaban I. Ahmed

“…Using the perturbation method and Mathematica software, we derived semi-analytical solutions for the governing partial differential equations in their complex form. nanoparticle-enhanced blood exhibits improved thermal performance compared to pure fluid, with the type and concentration of nanoparticles (Fe3O4, Au, SWCNTs) significantly impacting heat dissipation and temperature distribution within the microfluidic conduit. …”
Get full text

FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
Get full text

A Methodology for Practical Design and Optimization of Class-E DC-DC Resonant Converters by Andrea Celentano, Fabio Pareschi, Victor R. Gozalez-Diaz, Riccardo Rovatti, Gianluca Setti

“…Its peculiarity is to be dimensionless and based on the exact solution of the system of differential equations regulating the behavior of the circuit, ensuring very high precision and reliability with respect to all methodologies previously proposed by the state-of-the-art and based on the so-called sinusoidal approximation. …”
Get full text

A Multibody Model of Tilt-Rotor Aircraft Based on Kane’s Method by Jianmin Su, Chengyue Su, Sheng Xu, Xiaoxing Yang

“…The generalized active forces and generalized inertial forces of both the body and the nacelles (with rotors) are obtained, respectively, and the first-order differential equations of the generalized rates are obtained. …”
Get full text

Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection by Iyoko M.O., Olajuwon B.I., Fagbemiro O., Raji M.T.

“…The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. …”
Get full text

MOVIMENTO BROWNIANO: APLICAÇÃO EM ESTRATÉGIAS DE BUSCA by Matheus Dias Carvalho, Ricardo de Carvalho Falcão, Antonio Marcos de Oliveira Siqueira

“…This paper structured partial differential equations governing this process for the immortal case of walker, and later found analytical solutions to these expressions. …”
Get full text

Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. …”
Get full text

Using Nonlinear Diffusion Model to Identify Music Signals by Qiang Li

“…In this paper, combined with the partial differential equation music signal smoothing model, a new music signal recognition model is proposed. …”
Get full text

New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
Get full text

Stochastic Diffusive Modeling of CO₂ Emissions with Population and Energy Dynamics by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Hisham M. Al-Khawar, Yasir Nawaz

“…A novel numerical scheme, an extension of the Euler-Maruyama algorithm, is proposed to solve stochastic time-dependent partial differential equations governing the model. The scheme's consistency and stability are rigorously analyzed in the mean square sense. …”
Get full text

An integrated toolbox for creating neuromorphic edge applications by Lars Niedermeier, Nikil Dutt, Jeffrey L Krichmar

“…For instance, the mathematical foundation involves differential equations rather than basic activation functions. …”
Get full text