Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate by Chun Lu

“…Finally, we propose a definition of the solution to an impulsive stochastic functional differential equation with Markovian switching (ISFDM).…”
Get full text

The Rayleigh quotient and dynamic programming by Richard Bellman

“…The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. …”
Get full text

Application of PDE Constrained Optimization in Internal Combustion Engine Pollution Control by Hongliang Guan

“…Aiming at the problem of secondary pollution of waters due to the difficulty of controlling the dosage of purifiers in the treatment of internal combustion engine pollution, a partial differential equation (referred to as PDE) constrained optimization algorithm based on l1-norm is proposed. …”
Get full text

Reducing the sign problem with line integrals by Rasmus N. Larsen

“…We lay out how to write down an ordinary differential equation for the line integrals. As an example of its usage, we apply the results to a 1d quantum mechanical anharmonic oscillator with a x 4 potential in real time, finite temperature.…”
Get full text

The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation by Chunyan Liu

“…First, the fractional order generalized Pochhammer–Chree equation is transformed into an ordinary differential equation. Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. …”
Get full text

Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term by Rui Cao

“…A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. …”
Get full text

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. …”
Get full text

Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption by O. D. Makinde

“…The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. …”
Get full text

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). …”
Get full text

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.…”
Get full text

Taking into account the lens geometric distortion during accumulation of blurred star images in an astro-inertial attitude sensor by S. N. Vasilyuk

“…The analytical approach uses a model of direct distortion correction, which makes it possible to obtain a new differential equation for the blur trajectory in the image plane with distortion. …”
Get full text

Uniformly Convergent Nonpolynomial Spline Method for Singularly Perturbed Robin-Type Boundary Value Problems with Discontinuous Source Term by Habtamu Garoma Debela, Gemechis File Duressa

“…In this paper, a singularly perturbed second-order ordinary differential equation with discontinuous source term subject to mixed-type boundary conditions is considered. …”
Get full text

Synchronization of the Coupled Distributed Parameter System with Time Delay via Proportional-Spatial Derivative Control by Kun Yuan, Abdulaziz Alofi, Jinde Cao, Abdullah Al-Mazrooei, Ahmed Elaiw

“…By combining parabolic partial differential equation (PDE) theory with Lyapunov technique, the synchronization is studied for a class of coupled distributed parameter systems (DPS) described by PDEs. …”
Get full text

Determination of the response of a class of nonlinear time invariant systems by Sudhangshu B. Karmakar

“…The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. …”
Get full text

Analytical Models for Gravitating Radiating Systems by B. P. Brassel, S. D. Maharaj, G. Govender

“…We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. …”
Get full text

Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme by Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh, Getachew Adamu Derese

“…This paper proposes a new fitted operator strategy for solving singularly perturbed parabolic partial differential equation with delay on the spatial variable. …”
Get full text

On the Korteweg-de Vries equation: an associated equation by Eugene P. Schlereth, Ervin Y. Rodin

“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
Get full text

Mathematical Modeling of the Transmission Dynamics of Gumboro Disease by J. S. Musaili, I. Chepkwony, W. N. Mutuku

“…The basic reproduction number Rog is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever Rog<1 and an asymptotic stable EE whenever Rog>1. …”
Get full text

Obtaining the Soliton Type Solutions of the Conformable Time-Fractional Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity by Using Two Kinds of Kudryashov Methods by Arzu Akbulut

“…Thus, using the suitable wave transform, the given equation is converted into an ordinary differential equation. Then, the proposed methods are applied to the reduced equation. …”
Get full text

ON APPLICATION OF ARTIFICIAL NEURAL NETWORKS FOR MODELING OF WATER CONSUMPTION by Alexander N. Salugin, Roman N. Balkushkin

“…The use of mathematical models in the form of a system of differentiated equations is hampered by the uncertainty of the coefficients in their right-hand sides, which describe the intensities of processes of different natures: precipitation, water consumption by various sectors of the water management complex, water runoff during snow melting, transpiration, infiltration, etc. …”