Design of a Dynamic Simulator for a Biped Robot by Diego A. Bravo M, Carlos F. Rengifo Rodas

“…The intermittent nature of these forces and the mathematical inequalities that they must satisfy lead to models described by hybrid algebraic differential equations. In this paper, a simulator was developed for a seven degrees of freedom planar biped robot, which was modeled using the Euler-Lagrange formulation. …”
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Noether symmetry of multi-delay Birkhoffian system and its conserved quantity by Xin-Yu Du, Xiang-Hua Zhai

“…The multi-delay differential equations of motion are derived for both Birkhoffian and Hamiltonian models. …”
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Transient disturbances in a relaxing thermoelastic half space due to moving internal heat source by Sarbani Chakravorty, Amitava Chakravorty

“…The problem is reduced to the solution of three differential equations, one involving the elastic vector potential, and the other two coupled, involving the thermoelastic scalar potential and the temperature. …”
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The effect of time delay in plant--pathogen interactions with host demography by Bruno Buonomo, Marianna Cerasuolo

“…We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. …”
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Physics Informed by Deep Learning: Numerical Solutions of Modified Korteweg-de Vries Equation by Yuexing Bai, Temuer Chaolu, Sudao Bilige

“…The method that we used in this paper had demonstrated the powerful mathematical and physical ability of deep learning to flexibly simulate the physical dynamic state represented by differential equations and also opens the way for us to understand more physical phenomena later.…”
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A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator by Ahmed Sami Abdulghafour, Raid Kamel Naji

“…The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. …”
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Thermal Radiation and Buoyancy Effects on Heat and Mass Transfer over a Semi-Infinite Stretching Surface with Suction and Blowing by S. Shateyi

“…Appropriate transformations were employed to transform the governing differential equations to nonsimilar form. The transformed equations were solved numerically by an efficient implicit, iterative finite-difference scheme. …”
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Mixed Convection over an Inclined Wavy Surface in a Nanofluid Saturated Non-Darcy Porous Medium with Radiation Effect by Darbhasayanam Srinivasacharya, Poshala Vijay Kumar

“…The governing equations are transformed into a set of ordinary differential equations using the appropriate similarity transformation and then solved using the successive linearization method. …”
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Novel Stability Criteria of Nonlinear Uncertain Systems with Time-Varying Delay by Yali Dong, Shengwei Mei, Xueli Wang

“…By constructing the proposed Lyapunov-Krasovskii functional approach, continuous state feedback controllers are put forward, and the criteria which guarantee the exponential stabilization of the nonlinear systems with uncertainties and time-varying delay are established in terms of solutions to the standard Riccati differential equations. Furthermore, based on the Lyapunov method and the linear matrix inequality approach, the sufficient conditions of exponential stability for a class of uncertain systems with time-varying delays and nonlinear perturbations are derived. …”
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Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation by Dianchen Lu, Chen Yue, Muhammad Arshad

“…At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.…”
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Computing the Electric and Magnetic Matrix Green’s Functions in a Rectangular Parallelepiped with a Perfect Conducting Boundary by V. G. Yakhno, Ş. Ersoy

“…This method is based on approximation (regularization) of the Dirac delta function and its derivatives, which appear in the differential equations for magnetic and electric Green’s functions, and the Fourier series expansion meta-approach for solving the elliptic boundary value problems. …”
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Mathematical Modelling of the Transmission of Malaria. by Atubangire, Felix

“…The model takes in the ordinally differential equations. The basic reproduction number Ro is obtained. …”
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A Mathematical Model for the Dynamics of Income Distribution in the Presence of Production by Maria Letizia Bertotti

“…The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. …”
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A Generalized Approach of Triple Integral Transforms and Applications by Rania Saadeh

“…We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.…”
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A Multiresolution PDE-Based Deformable Surface for Medical Imaging Applications

“…<p>We recently developed a multiresolution PDE-based deformable surface whose deformation behavior is governed by partial differential equations (PDEs) such as the weighted minimal surface flow. …”
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Numerical Solutions for the Eighth-Order Initial and Boundary Value Problems Using the Second Kind Chebyshev Wavelets by Xiaoyong Xu, Fengying Zhou

“…A collocation method based on the second kind Chebyshev wavelets is proposed for the numerical solution of eighth-order two-point boundary value problems (BVPs) and initial value problems (IVPs) in ordinary differential equations. The second kind Chebyshev wavelets operational matrix of integration is derived and used to transform the problem to a system of algebraic equations. …”
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Linear algebra and differential geometry on abstract Hilbert space by Alexey A. Kryukov

“…The formalism itself and its applications in linear algebra, differential equations, and differential geometry are carefully analyzed.…”
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Research of Crawl Phenomenon of Chain Propulsion Equipment by Zhai Wang, Liu Jia, Qin Li

“…According to the structure characteristics of the equipment,the chain is regarded as an elastic element,also considering the polygon effect when the sprocket wheel rotates,the motion differential equations are set up. Based on the solving result,the impacts of chain stiffness,sprocket parameter on the velocity of the load is analyzed. …”
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Stochastic Predator-Prey System Subject to Lévy Jumps by Xinzhu Meng, Xiaohong Wang

“…In addition, we obtain the sufficient conditions for almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, we discuss the biological implications of the main results and show that the large noise can make the system go extinct. …”
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Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity by Keimer, Alexander, Pflug, Lukas

“…This fixed-point problem itself necessitates the study of existence, uniqueness and stability of a class of discontinuous ordinary differential equations. On the ODE level, we compare the solution type defined here with the well-known Carathéodory and Filippov solutions.…”
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