Quantum Tunnelling for Hawking Radiation from Both Static and Dynamic Black Holes by Subenoy Chakraborty, Subhajit Saha

“…It is found that different order correction terms satisfy identical differential equation and are solved by a typical technique. …”
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A mathematical model of weight change with adaptation by Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin

“…Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting by Mustafa Hasanbulli, Svitlana P. Rogovchenko, Yuriy V. Rogovchenko

“…We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. …”
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Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings by Xinlei Yi, Wenlian Lu, Tianping Chen

“…We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. …”
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Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method by Song Fu, Yun-Hua Zhang, Si-Yuan He, Xi Chen, Guo-Qiang Zhu

“…In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. …”
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A Study of the Impact of Underground Economy on Integral Tax Burden in the Proportional Growth Model under Uncertainty by Akif Musayev, Aygun Musayeva

“…It is also assumed that dynamics of gross domestic product are modeled by fuzzy linear differential equation. An optimal value of tax burden is determined as a solution to the considered fuzzy integral equation. …”
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Effect of time delay on a detritus-based ecosystem by Nurul Huda Gazi, Malay Bandyopadhyay

“…Next, we have introduced discrete time delay due to recycling of dead organic matters and gestation of nutrients to the growth equations of various trophic levels. With delay differential equation model system we have studied the effect of time delay on the stability behaviour. …”
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Modified Homotopy Perturbation Method and Approximate Solutions to a Class of Local Fractional Integrodifferential Equations by Bo Xu, Sheng Zhang

“…In this paper, the local fractional version of homotopy perturbation method (HPM) is established for a new class of local fractional integral-differential equation (IDE). With the embedded homotopy parameter monotonously changing from 0 to 1, the special easy-to-solve fractional problem continuously deforms to the class of local fractional IDE. …”
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Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions by Yan Zhang, Peibiao Zhao

“…Moreover, applying the dual method along with the partial differential equation method, we verify the asymptotic behavior of the optimal control strategy, which means that the optimal investment-reinsurance strategy with the general utility functions converges to that with the power utility function at any level of the initial wealth.…”
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Global attractivity of positive periodic solutions for an impulsive delay periodic food limited population model by Jian Song

“…We will consider the following nonlinear impulsive delay differential equation N′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e. t>0, t≠tk, N(tk+)=(1+bk)N(tk), K=1,2,…, where m is a positive integer, r(t), K(t), λ(t) are positive periodic functions of periodic ω. …”
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Numerical Solutions to Optimal Portfolio Selection and Consumption Strategies under Stochastic Volatility by Lei Ge, Qiang Zhang

“…Based on the method of dynamic programming, this paper uses analysis methods governed by the nonlinear and inhomogeneous partial differential equation to study modern portfolio management problems with stochastic volatility, incomplete markets, limited investment scope, and constant relative risk aversion (CRRA). …”
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Coefficients of prolongations for symmetries of ODEs by Ricardo Alfaro, Jim Schaeferle

“…He found that transformations which form a continuous group and leave a differential equation invariant can be used to simplify the equation. …”
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Traverse Vibration of Axially Moving Laminated SMA Beam considering Random Perturbation by Hao Ying, Gao Minglei

“…The transverse vibration differential equation of axially moving SMA laminated beam with two simply-supported edges is obtained through the Galerkin method. …”
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Optimal Strategies for Control of COVID-19: A Mathematical Perspective by Baba Seidu

“…A deterministic ordinary differential equation model for SARS-CoV-2 is developed and analysed, taking into account the role of exposed, mildly symptomatic, and severely symptomatic persons in the spread of the disease. …”
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Lyapunov Stability of the Generalized Stochastic Pantograph Equation by Ramazan Kadiev, Arcady Ponosov

“…The framework can be applied to any stochastic functional differential equation with finite dimensional initial conditions.…”
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Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias by Dumitru I. Caruntu, Kyle N. Taylor

“…The method of multiple scales (MMS) is used to solve the dimensionless differential equation of motion of the resonator and find the steady-state solutions. …”
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Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising by V. B. Surya Prasath, Arindama Singh

“…We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of anisotropic diffusion. …”
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Orthogonal Polynomials on Radial Rays in the Complex Plane: Construction, Properties and Applications by Gradimir V. Milovanović

“…Recurrence relations for such kinds of orthogonal polynomials and their zero distribution, as well as a connection with the standard polynomials orthogonal on the real line, are derived, including the corresponding linear differential equation of the second order. Finally, some applications in physics and electrostatics are mentioned.…”
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An Extended Newmark-FDTD Method for Complex Dispersive Media by Yu-Qiang Zhang, Peng-Ju Yang

“…In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. …”
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