Investigation of properties of system of automatic control of liquid-propellant rocket propulsion system with integrating regulator by I. A. Kyzmenko, A. B. Yakovlev

“…There are obtained differential equations describing the operation of the comparison element, the throttle valve, the hydraulic amplifier, and the processes in the gas generator. …”
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Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy by Haiyang Wang, Zhen Wu

“…We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. …”
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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. …”
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Vibrations of Plates and Shells with Attached Mass by L. U. Sultanov, I. R. Garifullin

“…The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. …”
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A Mathematical Model For The Population Dynamics Of Disease Transmiting Vectors in Particular Female Anopheles Mosquitoes. by Turyamusiima, Richard

“…The mosquito free equilibrium and endemic equilibrium have been determined by setting system of ordinary differential equations to zero. Basic reproduction has been determined using the next generation matrix management analyzed. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. …”
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Chemical reactions with the Casson nanofluid flow by the bioconvective behavior of microorganisms over a spinning disc by Prabhakar Sagadevan, Umadevi Raju, Meganathan Murugesan, Unai Fernandez-Gamiz, Samad Noeiaghdam

“…Using the right variables to change the nonlinear partial differential equations (PDEs) that govern the problem into a system of ordinary differential equations (ODEs) is a key step toward finding numerical solutions. …”
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Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems by Hassan Saberi Nik, Paulo Rebelo

“…The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. …”
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Stoichiometric Plant-Herbivore Models and Their Interpretation by Yang Kuang, Jef Huisman, James J. Elser

“…Our model takes the simple form of asystem of two autonomous ordinary differential equations. It canbe shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. …”
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Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane by H. K. Mondal, T. K. Chaudhury

“…Velocity distribution is also obtained for certain values of the parameters by integrating the coupled differential equations by Runge-Kutta method and compared with the analytical solution. …”
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Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method by Berna Bülbül, Mehmet Sezer

“…We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. …”
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Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay by Lixia Zuo, Maoxing Liu

“…The model is analyzed by using stability theory of differential equations and numerical simulations. Both equilibria have been proved to be globally asymptotically stable. …”
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New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems by K. W. Moo, N. Senu, F. Ismail, M. Suleiman

“…Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. …”
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On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems by Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak

“…Such models frequently take the form of a set ofnonlinear ordinary differential equations. While the model is continuous-time,the performance index, used in the fitting procedure, involves measurementstaken only at discrete-time moments. …”
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Computational modeling approaches to studying the dynamics of oncolytic viruses by Dominik Wodarz

“…This article reviews different mathematical modelingapproaches ranging from ordinary differential equations to spatiallyexplicit agent-based models. …”
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Some new existence results of positive solutions for anisotropic variable exponent operator by Rafik Guefaifia, Salah Boulaaras, Rashid Jan

“…By deriving new existence results, the study advances the understanding of nonlinear partial differential equations in anisotropic and variable exponent settings. …”
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Semianalytical Solutions of Some Nonlinear-Time Fractional Models Using Variational Iteration Laplace Transform Method by Javed Iqbal, Khurram Shabbir, Liliana Guran

“…In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. …”
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Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order by Yi Chai, Liping Chen, Ranchao Wu

“…By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. …”
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Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects by Jia-Fang Zhang

“…Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs).…”
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Almost Periodic Functions on Time Scales and Applications by Yongkun Li, Chao Wang

“…We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. …”
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