Convergence in Distribution of Some Self-Interacting Diffusions by Aline Kurtzmann

“…These diffusions are solutions to stochastic differential equations: dXt=dBt-g(t)∇V(Xt-μ¯t)dt, where μ¯t is the empirical mean of the process X, V is an asymptotically strictly convex potential, and g is a given positive function. …”
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Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations by A. H. Bhrawy, M. A. Alghamdi

“…A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. …”
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On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications by Teng-fei Li, Heng-you Lan

“…In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. …”
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A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems by A. H. Bhrawy, M. A. Alghamdi

“…We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. …”
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Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations) by Dimitrios E. Panayotounakos, Theodoros I. Zarmpoutis

“…We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs) of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions), as well as of the free member of the considered ODE; the parameter 𝜈 being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. …”
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Existence and Uniqueness Results for a Class of Singular Fractional Boundary Value Problems with the p-Laplacian Operator via the Upper and Lower Solutions Approach by KumSong Jong, HuiChol Choi, KyongJun Jang, SunAe Pak

“…In this paper, we study the existence and uniqueness of positive solutions to a class of multipoint boundary value problems for singular fractional differential equations with the p-Laplacian operator. Here, the nonlinear source term f permits singularity with respect to its time variable t. …”
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Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. …”
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Common Fixed-Point Results in Ordered Left (Right) Quasi-b-Metric Spaces and Applications by Hemant Kumar Nashine, Sourav Shil, Hiranmoy Garai, Lakshmi Kanta Dey, Vahid Parvaneh

“…Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.…”
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On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs by F. N. Koumboulis, M. G. Skarpetis, B. G. Mertzios

“…The Euler equations, namely a set of nonlinear partial differential equations (PDEs), mathematically describing the dynamics of inviscid fluids are numerically integrated by directly modeling the original continuous-domain physical system by means of a discrete multidimensional passive (MD-passive) dynamic system, using principles of MD nonlinear digital filtering. …”
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A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method by R. Ellahi

“…Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. …”
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Sensitivity and Optimal Control Analysis of an Extended SEIR COVID-19 Mathematical Model by C. M. Wachira, G. O. Lawi, L. O. Omondi

“…In this paper, a mathematical model based on a system of ordinary differential equations is developed with vaccination as an intervention for the transmission dynamics of coronavirus 2019 (COVID-19). …”
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Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function by David W. Pravica, Njinasoa Randriampiry, Michael J. Spurr

“…They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials. …”
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Almost Sure Stability of Stochastic Neural Networks with Time Delays in the Leakage Terms by Mingzhu Song, Quanxin Zhu, Hongwei Zhou

“…By using the LaSalle invariant principle of stochastic delay differential equations, Itô’s formula, and stochastic analysis theory, some novel sufficient conditions are derived to guarantee the almost sure stability of the equilibrium point. …”
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An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform by Devendra Kumar, Jagdev Singh, A. Kılıçman

“…The results obtained by the two methods are in agreement, and, hence, this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of sumudu transform, homotopy perturbation method, and He’s polynomials. …”
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The numerical models of the estimation of the electrooptical parameters of GaAs by Albertas Pincevičius, Rimantas-Jonas Rakauskas, Svajonė Vošterienė

“…The system of the differential equations was solved by a method Gear with a modification of a step. …”
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Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem by R. J. Moitsheki, M. D. Mhlongo

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Optical vortices in dispersive nonlinear Kerr-type media by Lubomir M. Kovachev

“…The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. …”
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Dynamic Analysis on a Diffusive Two-Enterprise Interaction Model with Two Delays by Yanxia Zhang, Long Li

“…In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. Finally, numerical simulation experiments are conducted to illustrate the validity of the theoretical conclusions.…”
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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. …”
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