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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Convergence Time Calculation for Supertwisting Algorithm and Application for Nonaffine Nonlinear Systems by Jianhua Zhang, Quanmin Zhu, Yang Li

“…The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. …”
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Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation by Maria Ihsane El Bahi, Khalid Hilal

“…With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. …”
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Quasigeostrophic Equations for Fractional Powers of Infinitesimal Generators by Luciano Abadias, Pedro J. Miana

“…In this paper we treat the following partial differential equation, the quasigeostrophic equation: ∂/∂t+u·∇f=-σ-Aαf,  0≤α≤1, where (A,D(A)) is the infinitesimal generator of a convolution C0-semigroup of positive kernel on Lp(Rn), with 1≤p<∞. …”
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The Generalized Hermite Spectral Method Combined with Laplace Transform for Solution of the Time Fractional Fokker–Planck Equation by Lu-feng Yang

“…By the Laplace transform, the ordinary differential equation about the orthogonal expansion coefficient is transformed into a linear algebraic equation system, with the coefficient matrix being a tridiagonal lower triangular matrix. …”
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A model of regulatory dynamics with threshold-type state-dependent delay by Qingwen Hu

“…A general model which is an extension of the classical differential equation models with constant or zero time delays is developed to study the stability of steady state, the occurrence and stability of periodic oscillations in regulatory dynamics. …”
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Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization by Lei Hu

“…The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. …”
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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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Disease dynamics for the hometown of migrant workers by Ram P. Sigdel, C. Connell McCluskey

“…Biol. 300:100--109 (2012) formulatedand studied a delay differential equation model for disease dynamics in a region where a portionof the population leaves to work in a different region for an extended fixed period. …”
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Dynamical Analysis for the Hybrid Network Model of Delayed Predator-Prey Gompertz Systems with Impulsive Diffusion between Two Patches by Li Xiang, Yurong Zhang, Dan Zhang, Zhichun Yang, Lingzhi Huang

“…Furthermore, by employing the theory of delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the network.…”
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Positive Solutions for the Initial Value Problems of Fractional Evolution Equation by Yue Liang, Yu Ma, Xiaoyan Gao

“…As an example, we study the partial differential equation of parabolic type of fractional order.…”
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Approximate Symmetries Analysis and Conservation Laws Corresponding to Perturbed Korteweg–de Vries Equation by Tahir Ayaz, Farhad Ali, Wali Khan Mashwani, Israr Ali Khan, Zabidin Salleh, Ikramullah

“…The Korteweg–de Vries (KdV) equation is a weakly nonlinear third-order differential equation which models and governs the evolution of fixed wave structures. …”
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Analytic Approximate Solution for Falkner-Skan Equation by Vasile Marinca, Remus-Daniel Ene, Bogdan Marinca

“…This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. …”
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The effects of heterogeneity on Darcy-Benard convection saturated with a ferrofluid by Moussa Rachida, Lagziri Hajar, El Khanoussi Fadoua, El Fakiri Hanae

“…A dimensionless formulation and linear stability analysis are employed to derive an ordinary differential equation, which is solved using the shooting method and a Runge-Kuttasolver. …”
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The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems by Yanling Shi, Jia Li

“…We study the following two-order differential equation, (Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0, where Φp(s)=|s|(p-2)s, p>0. f(x,t) and g(x,t) are real analytic functions in x and t, 2aπp- periodic in x, and quasi-periodic in t with frequencies (ω1,…,ωm). …”
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A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs by I. B. Aiguobasimwin, R. I. Okuonghae

“…In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). …”
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Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments by S. Shao, C. L. Chang

“…After defining the process of conditional probability in finite time, martingale theory turns the nonlinear stochastic differential equation to a special class of boundary value problems defined by a parabolic equation with a nonsmooth coefficient of the convection term. …”
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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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New Exact Solutions of Burgers’ Equation Using Power Index Method by Khalil Ahmad, Khudija Bibi

“…In this method, we choose suitable indexes of independent variables and similarity transformation so that the partial differential equation may be converted into ODE. We have obtained analytic solution of the ODE by using symbolic package Maple. …”
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