Representation of the solution of a nonlinear molecular beam epitaxy equation by Boubaker Smii

“…Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. …”
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Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation by Zhengwen Yin, Yuanshun Tan

“…In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. …”
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Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels by Salvatore Brischetto

“…The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. …”
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Pharmacodynamics of interspecies interactions in polymicrobial infections by C. Herzberg, J. G. C. van Hasselt

“…To this end, we developed an in silico model which combined agent-based modeling with ordinary differential equations. Our analyses suggest that both interspecies interactions, modifying either drug sensitivity or bacterial growth rate, and drug-specific pharmacological properties drive the bacterial pharmacodynamic response. …”
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Liquid Sloshing in a Horizontal Circular Container with Eccentric Tube under External Excitation by Mohammad Nezami, Mohammad Mehdi Mohammadi, Atta Oveisi

“…The resulting linear sets of ordinary differential equations are truncated and then solved numerically by employing Laplace transform technique followed by Durbin’s numerical inversion pattern. …”
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On an Interpolation Based Spectral Homotopy Analysis Method for PDE Based Unsteady Boundary Layer Flows by S. S. Motsa

“…This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. …”
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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α∈0,1 and different step sizes h. …”
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Dynamics of Terrorism in Contemporary Society for Effective Management by Kazeem Babatunde Akande, Julius Adebowale Makinde, Mohammed Olanrewaju Ibrahim

“…Mathematical modelling of epidemiology was conceptualized for the model formulation, and the resulting autonomous differential equations were critically analyzed with the Lipschitz condition, next generation matrix, and Bellman and Cooke’s criteria for the management of insurgency in the society. …”
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A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation by E. Momoniat

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GOLD VALUE WITH TRADABLE AND NON-TRADABLE GOODS IN A MULTI-COUNTRY GROWTH MODEL WITH FREE TRADE by Wei-Bin Zhang

“…We show that the dynamics of the J -country world economy can be described by J differential equations. We simulate the model to demonstrate the existence of an equilibrium point, motion of the dynamic system, and (local) stability of the equilibrium point. …”
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Mathematical Modeling and Analysis of TB and COVID-19 Coinfection by Kassahun Getnet Mekonen, Shiferaw Feyissa Balcha, Legesse Lemecha Obsu, Abdulkadir Hassen

“…This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. …”
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GOLD VALUE WITH TRADABLE AND NON-TRADABLE GOODS IN A MULTI-COUNTRY GROWTH MODEL WITH FREE TRADE by Wei-Bin Zhang

“…We show that the dynamics of the J -country world economy can be described by J differential equations. We simulate the model to demonstrate the existence of an equilibrium point, motion of the dynamic system, and (local) stability of the equilibrium point. …”
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Natural Frequency Analysis of Two Nonlinear Panels Coupled with a Cavity Using the Approximate Elliptic Integral Solution and the Method of Harmonic Residual Minimization by Y. Y. Lee

“…A multistructural/acoustic modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibrations of the flexible panels and acoustic pressure induced within the air gap. …”
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Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques by Imran Siddique, Khush Bukht Mehdi, M. Ali Akbar, Hamiden Abd El-Wahed Khalifa, Asim Zafar

“…These methods can also be used to extract the novel exact traveling wave solutions for solving any types of integer and fractional differential equations arising in mathematical physics.…”
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Implementing the Vieta–Lucas Collocation Optimization Method for MHD Casson and Williamson Model under the Effects of Heat Generation and Viscous Dissipation by M.M. Khader, A. Eid, M. Adel

“…This method is used to convert the problem’s system of ordinary differential equations (ODEs) into a nonlinear system of algebraic equations. …”
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On Fourier Series of Fuzzy-Valued Functions by Uğur Kadak, Feyzi Başar

“…Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. …”
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A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate by Nadia Mohdeb

“…Design/methodology/approach – The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion. …”
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Modeling and Analysis of Unsteady Casson Fluid Flow due to an Exponentially Accelerating Plate with Thermal and Solutal Convective Boundary Conditions by Mehari Fentahun Endalew, Subharthi Sarkar

“…Fundamental equations governing an isotropic incompressible radiative Casson fluid flow are defined through a set of linear partial differential equations, and exact solutions are derived by using the Laplace transform approach. …”
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Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops by Fengwei Yin, Guanwei Luo, Xueming Wang

“…The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. …”
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Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations by Alvaro H. Salas, Wedad Albalawi, M. R. Alharthi, S. A. El-Tantawy

“…In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations (ODEs) that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. …”
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