An Improved Cockroach Swarm Optimization by I. C. Obagbuwa, A. O. Adewumi

“…The original CSO was modelled with three components: chase-swarming, dispersion, and ruthless; additional hunger component which is modelled using partial differential equation (PDE) method is included in this paper. …”
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Analytical Solutions for Nonlinear Dispersive Physical Model by Wen-Xiu Ma, Mohamed R. Ali, R. Sadat

“…The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. …”
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DYNAMIC PERFORMANCE ANALYSIS OF SCISSOR SEAT SUSPENSION SYSTEM by MA MingMing, YU HuiJie, NI WeiYu, WANG HaiHua

“…Based on D' Alembert's principle, the differential equation of the motion about the system was deduced, and the transfer function of the system was obtained by the basis of estabishing virtual equilibrium state of a seat suspension system. …”
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An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing by R. Company, V. N. Egorova, L. Jódar

“…This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. …”
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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. …”
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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. …”
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Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G)-Expansion Method by Muhammad Shakeel, Qazi Mahmood Ul-Hassan, Jamshad Ahmad, Tauseef Naqvi

“…This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. …”
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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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Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model by Huidong Cheng, Fang Wang, Tongqian Zhang

“…According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. …”
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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. …”
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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).…”
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Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods by H. Vazquez-Leal, K. Boubaker, L. Hernandez-Martinez, J. Huerta-Chua

“…Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.…”
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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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Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions by Hui Li, Libo Wang, Minghe Pei

“…We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)), t∈[0,1], x(0)=x′(1)=0, x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds, x′′′(1)=0, where f∈C([0,1]×ℝ4), h∈C([0,1]×ℝ3). …”
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Hopf Bifurcation in a Cobweb Model with Discrete Time Delays by Luca Gori, Luca Guerrini, Mauro Sodini

“…The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.…”
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Selective Extraction of Entangled Textures via Adaptive PDE Transform by Yang Wang, Guo-Wei Wei, Siyang Yang

“…Selective extraction of entangled textures is a challenging task due to spatial entanglement, orientation mixing, and high-frequency overlapping. The partial differential equation (PDE) transform is an efficient method for functional mode decomposition. …”
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RESEARCH ON NONLINEAR VIBRATION FOR ELECTRICALLY ACTUATED SINGLE-WALLED CARBON NANOTUBE by YANG ZhiAn, LIU ZhiWei

“…According to the beam theory,the nonlinear dynamic equation of carbon nanotube system is established,it is a nonlinear partial differential equation. By means of the method of multiple scales,nonlinear vibration equation of the system is acquired and the numerical calculation is carried out. …”
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Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices by Gashaye Dessalew, Tesfaye Kebede, Gurju Awgichew, Assaye Walelign

“…Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. …”
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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. …”
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ANALYSIS ON MAGNETO-AEROELASTIC TRANSVERSE VIBRATION OF ROTATING CONDUCTIVE CIRCULAR PLATE by HU YuDa, LI WenQiang

“…According to principles of electromagnetic field combined with a simplified aerodynamic model,the expressions of electromagnetic force and aerodynamic load of rotating circular plate were given.The magneto-aeroelastic free differential equation of conductive rotating circular plate was presented by means of Galerkin method. …”
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