Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme by Muhammad Nadeem, Hanan A. Wahash

“…The fractional differential equation may be transformed into its partner equation using He’s fractional complex transform, and then, the nonlinear elements can be readily handled using the homotopy perturbation method (HPM). …”
Get full text

Computer-Aided Numerical Inversion of Laplace Transform by Umesh Kumar

“…This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.…”
Get full text

Preliminary analysis of an agent-based model for a tick-borne disease by Holly Gaff

“…The results from this model arecompared with those from previously published differential equation based populationmodels. The findings show that the agent-based model produces significantly lower prevalenceof disease in both the ticks and their hosts than what is predicted by a similardifferential equation model.…”
Get full text

Mathematical Model for The Transmission of Malaria In Uganda. by Lusambya, Robert

“…The resent an ordinary differential equation mathematical model for the spread of malaria in Mosquito populations. …”
Get full text

Kinetic Analysis for Macrocyclizations Involving Anionic Template at the Transition State by Vicente Martí-Centelles, M. Isabel Burguete, Santiago V. Luis

“…The corresponding differential equation systems for each kinetic model can be solved numerically. …”
Get full text

Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect by Wenjie Hu, Hua Zhao, Tao Dong

“…Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. …”
Get full text

Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments by Cristóbal González, Antonio Jiménez-Melado

“…In the case of q(t,s)=(t-s)+, its solutions with asymptotic behavior given by ω(t) yield solutions of the second order nonlinear abstract differential equation y''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0, with the same asymptotic behavior at ∞ as ω(t).…”
Get full text

Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient by Te-Wen Tu, Sen-Yung Lee

“…By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. …”
Get full text

Ring-Shaped Potential and a Class of Relevant Integrals Involved Universal Associated Legendre Polynomials with Complicated Arguments by Wei Li, Chang-Yuan Chen, Shi-Hai Dong

“…We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. …”
Get full text

Neural-Network-Based Approach for Extracting Eigenvectors and Eigenvalues of Real Normal Matrices and Some Extension to Real Matrices by Xiongfei Zou, Ying Tang, Shirong Bu, Zhengxiang Luo, Shouming Zhong

“…Although the ordinary differential equation on which our proposed algorithm is built is only n-dimensional, it can succeed to extract n-dimensional complex eigenvectors that are indeed 2n-dimensional real vectors. …”
Get full text

Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions by A. Beléndez, M. L. Alvarez, J. Francés, S. Bleda, T. Beléndez, A. Nájera, E. Arribas

“…To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. …”
Get full text

Stiffness Calculation for Negative Moment Region of Steel-Concrete Composite Beams considering the Influence of Cracking and Interface Slip by Wenlong Cao, Jianqing Bu, Cunbao Zhao, Xueyan Wang, Liping Zhang, Jiren Zhang

“…To evaluate this decrease in the stiffness of SCCBs, a static differential equation is used to derive analytical expressions of interface slip and deflection. …”
Get full text

An Adaptive Time-Stepping Algorithm for the Allen–Cahn Equation by Chaeyoung Lee, Jintae Park, Soobin Kwak, Sangkwon Kim, Yongho Choi, Seokjun Ham, Junseok Kim

“…The AC equation is a nonlinear partial differential equation, which was first proposed by Allen and Cahn for antiphase boundary motion and antiphase domain coarsening. …”
Get full text

Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process by Hao Chang, Xi-min Rong

“…Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. …”
Get full text

Dynamic Responses of an Overhead Crane’s Beam Subjected to a Moving Trolley with a Pendulum Payload by Huasen Liu, Wenming Cheng, Yinqi Li

“…In this paper, the coupling system of an overhead crane was simplified to that of a moving mass with pendulum swing passing beam model. The differential equation motion of a coupled overhead crane system was derived based on the Lagrange equation. …”
Get full text

-Advanced Models for Tsunami and Rogue Waves by D. W. Pravica, N. Randriampiry, M. J. Spurr

“…A wavelet , that satisfies the q-advanced differential equation for , is used to model N-wave oscillations observed in tsunamis. …”
Get full text

Resonance Spectra of Caged Stringy Black Hole and Its Spectroscopy by I. Sakalli, G. Tokgoz

“…We then show how the complex resonant frequencies of the caged GHSBH are computed using the Bessel differential equation that arises when the scalar perturbations around the event horizon are considered. …”
Get full text

A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field by Abdul-Sattar J. A. Al-Saif, Abeer Majeed Jasim

“…The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. …”
Get full text

Per‐unit transformation for the combined analysis of multi‐energy integration by Zhang Zhang, Fei Wang, Hui Fan

“…Abstract To handle numerical issues caused by dimensional differences among heterogeneous states in integrated energy systems (IES), this paper proposes a novel per‐unit transformation method and explores its applications to the partial differential equation‐governed models. Initially, a unified IES model is developed, which encompasses both fast and slow dynamics in a generalized form. …”
Get full text

Theoretical Vibration Analysis Regarding Excitation due to Elliptical Shaft Journals in Sleeve Bearings of Electrical Motors by Ulrich Werner

“…The solution of the linear differential equation system leads to the mathematical description of the movement of the rotor mass, the shaft journals, and the sleeve bearing housings. …”
Get full text