Weyl-Euler-Lagrange Equations of Motion on Flat Manifold by Zeki Kasap

“…In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. …”
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Contrast Expansion Method for Elastic Incompressible Fibrous Composites by Piotr Drygaś, Vladimir Mityushev

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Elastic Equilibrium of Porous Cosserat Media with Double Porosity by Roman Janjgava

“…The corresponding three-dimensional system of differential equations is derived. Detailed consideration is given to the case of plane deformation. …”
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An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations by Hooman Darvishi, M. T. Darvishi

“…These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. …”
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Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy by Qizhen Xiao, Binxiang Dai

“…We firstly show the existence of order-$1$ heteroclinic cycle and order-$1$ positive periodic solutions by using the geometric theory of differential equations for the unperturbed system. Based on the theory of rotated vector fields, the order-$1$ positive periodic solutions and heteroclinic bifurcation are studied for the perturbed system. …”
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Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions by Yan Gao, Songlin Liu

“…In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. In this paper, various ways of numerical test calculations are prepared to evaluate performance of the fourth-order CFD and sixth-order CFD schemes, respectively, and the empirical results are proved to verify the effectiveness of the schemes in this paper.…”
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Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity by M. B. K. Moorthy, K. Senthilvadivu

“…The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. …”
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Analysis of electroelastic frictionless contact problems with adhesion by Mircea Sofonea, Rachid Arhab, Raafat Tarraf

“…The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.…”
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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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Analysis of the Dynamic Load Sharing Characteristic of Two-stage Planetary Transmission by Li Siqian, Wu Shijing, Wang Xiaosun

“…To study the dynamic load sharing characteristics of two- stage planetary gear train,a translation- torsion coupling dynamics model is established by taking the nonlinear factors like time- varying mesh stiffness,position error,eccentric error,gear backlash and coupling stiffness into account,and the dimensionless dynamics differential equations for the system are derived and solved by numerical method. …”
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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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