Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions by Douglas R. Anderson, Christopher C. Tisdell

“…Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. …”
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Modeling the motion of a ship with suspended cargo by Solovyov A. A., Shugay S. N.

“…When solving problems of dynamics, mathematical models of the roll of a vessel with suspended cargo in calm water and regular waves have been proposed, and linear differential equations of the roll of a vessel with suspended cargo have been obtained. …”
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Nonlinear Vibration of a Continuum Rotor with Transverse Electromagnetic and Bearing Excitations by Haiyang Luo, Yuefang Wang

“…The governing equation of motion is derived and discretized as a group of ordinary differential equations using the Galerkin's method. The stability of the equilibrium of the rotor is analyzed with the Routh-Hurwitz criterion and the occurrence of the Andronov-Hopf bifurcation is pointed out. …”
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Dynamic Response of Shear-Flexible Cylindrical Isotropic Shells with Clamped Edges by Zafer I. Sakka, Jamal A. Abdalla, H.R.H. Kabir

“…The Sander’s kinematic relations for moderately thick cylindrical shell panels are utilized to develop the governing partial differential equations in conjunction with the boundary conditions. …”
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Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations. by Akhtar Hussain, M Usman, Fiazuddin Zaman, Ahmed M Zidan, Jorge Herrera

“…The Lie group method is a powerful technique for obtaining analytical solutions for various nonlinear differential equations. This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical properties using Lie group invariants. …”
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Novel Evaluation of Fuzzy Fractional Helmholtz Equations by Meshari Alesemi, Naveed Iqbal, Noorolhuda Wyal

“…It is critical to emphasize that the purpose of the proposed fuzziness approach is to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations that arise in complex and physical structures.…”
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Investigation of Nonlinear Vibrational Analysis of Circular Sector Oscillator by Using Cascade Learning by Naveed Ahmad Khan, Muhammad Sulaiman, Jamel Seidu, Fahad Sameer Alshammari

“…This paper analyzed the model of swinging oscillation of a solid circular sector arising in hydrodynamical machines, electrical engineering, heat transfer applications, and civil engineering. Nonlinear differential equations govern the mathematical model for frequency oscillation of the system. …”
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Research on Error Propagation Law of Flood Routingby Fourth-order Runge - Kutta Method by ZHOU Bin

“…The fourth-order Runge-Kutta method is one of the commonly used algorithms for solvingordinary differential equations of reservoir flood routing. Studying its error propagation law isof great significance for improving the accuracy of results. …”
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Numerical Solutions for Laminar Boundary Layer Nanofluid Flow along with a Moving Cylinder with Heat Generation, Thermal Radiation, and Slip Parameter by Titilayo Morenike Agbaje, Gilbert Makanda

“…The fluid mathematical model developed from the Navier-Stokes equations resulted in a system of partial differential equations which were then solved by the multidomain bivariate spectral quasilinearization method (MD-BSQLM). …”
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Flap/Lag Stall Flutter Control of Large-Scale Wind Turbine Blade Based on Robust H2 Controller by Tingrui Liu, Wei Xu

“…The aeroelastic partial differential equations are reduced by Galerkin method, with the aerodynamic forces decomposed by strip theory. …”
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Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method by Mohammad Alshammari, Wael W. Mohammed, Mohammed Yar

“…It is crucial to emphasize that the suggested fuzziness method is intended to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations found in complex and physical structures.…”
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ANTI-VIBRATION OPTIMIZATION DESIGN FOR CLAMP-LIFTING DEVICE ON AIRCRAFT TRACTORS by GAO QingZhen, HUANG An, SHI PeiCheng

“…In order to solve the vibration problem of clamp-lifting device, the joint mechanical analysis and modelings including clamp-lifting device, wheel and landing gear were carried out, and the system vibration differential equations including stiffness and damping characteristics of components were obtained by the frequency response method. …”
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Backward Anticipated Social Optima: Input Constraints and Partial Information by Shujun Wang

“…Furthermore, differently from the classic social optima literature, the dynamics in this framework are driven by <i>anticipated</i> backward stochastic differential equations (ABSDE) in which the <i>terminal</i> instead of the <i>initial</i> condition is specified and the anticipated terms are involved. …”
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Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization by Enas Suhail, Mahmoud El-Alem, Omar Bazighifan, Ahmed Zekri

“…Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. …”
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Insight on the complete process of photoacoustic generation and propagation of cerebrovascular in brain via multi-physics coupling method by Shangkun Hou, Anzhi Lv, Jiabin Lin, Bokang You, Shuaixin Huang, Xianlin Song

“…The diffusion equation is approximated by the partial differential equations in the form of coefficients in the mathematical module of COMSOL to describe laser propagation in brain tissue. …”
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Time-periodic dynamics in COVID-19 transmission considering the impact of population disbelief and fear by Mahmoud A. Ibrahim, Attila Dénes

“…Our model utilizes a system of differential equations that incorporates the impact of both contagious fear and contagious disbelief surrounding the disease on its transmission dynamics. …”
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A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing by Arthanari Ramesh, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. …”
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Modeling and simulation for toxicity assessment by Cristina Anton, Jian Deng, Yau Shu Wong, Yile Zhang, Weiping Zhang, Stephan Gabos, Dorothy Yu Huang, Can Jin

“…We consider a three dimensional system of differential equations with variables corresponding to the cell index, the intracellular concentration of toxicant, and the extracellular concentration of toxicant. …”
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Dubovsky’s Class of Mathematical Models for Describing Economic Cycles with Heredity Effects by Danil Makarov, Roman Parovik, Zafar Rakhmonov

“…Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. …”
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Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models by Divine Wanduku, Md Mahmud Hasan

“…The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. …”
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