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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THE RESEARCH OF LOCAL STABILITY FOR SIMPLY SUPPORTED SKEW PLATES IN THE CRANE by FU WeiGang, YAN Feng, LI Meng, CHENG WenMing

“…To study the buckling of bionics skew plates in the crane’s vein box girder,the dimensionless derivations of bucking balance differential equations for skew plates has been given when it is affected by the longitudinal load in the oblique coordinate,and the dimensionless equation of boundary conditions is also given. …”
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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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Heat transportation of 3D chemically reactive flow of Jeffrey nanofluid over a porous frame with variable thermal conductivity by Nahid Fatima, Aaqib Majeed, Taoufik Saidani, Nouman Ijaz, Kamal Barghout, Nidal Abu-Libdeh

“…To model these phenomena, we employ the boundary layer approximation to derive a system of partial differential equations (PDEs). These PDEs are subsequently simplified into more manageable ordinary differential equations (ODEs) using the similarity variables. …”
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Thermal enhancement using variable characteristics and tripartite diffusion features of solar aircraft wings in context of Reiner-Philippoff hybrid nanofluid passing through a para... by Esraa N. Thabet, A.M. Abd-Alla, S.M.M. El-Kabeir

“…With the utilization of the appropriate similarity transformations, partial differential equations that represent the mathematical model can be simplified to ordinary differential equations. …”
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Second order slip micropolar MHD hybrid nanofluid flow over a stretching surface with uniform heat source and activation energy: Numerical computational approach by Syed Arshad Abas, Hakeem Ullah, Mehreen Fiza, Ali Akgul, Aasim Ullah Jan, Magda Abd El-Rahman, Seham M. Al-Mekhlafi

“…These PDEs are subsequently transformed into a set of ordinary differential equations (ODEs) using similarity transformations. …”
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Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model by Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei

“…The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. …”
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Fixed Point Theory and the Liouville–Caputo Integro-Differential FBVP with Multiple Nonlinear Terms by Shahram Rezapour, Ali Boulfoul, Brahim Tellab, Mohammad Esmael Samei, Sina Etemad, Reny George

“…This work is reserved for the study of a special category of boundary value problems (BVPs) consisting of Liouville–Caputo integro-differential equations with multiple nonlinear terms. This fractional model and its boundary value conditions (BVCs) involve different simple BVPs, in which the second BVC as a linear combination of two Caputo derivatives of the unknown function equals a nonzero constant. …”
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Detection of the onset of numerical chaotic instabilities by lyapunov exponents by Alicia Serfaty De Markus

“…It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. …”
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Dinamic of blood pluripotential stem cell formation processes by Donatas Švitra, Renata Retkutė

“…With the help of difference-differential equations the processes of the PPSC production are modeled. …”
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Strain gradient elasticity within the symmetric BEM formulation by S. Terravecchia, T. Panzeca, C. Polizzotto

“…The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 1/ r 4 . …”
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Computational analysis for fractional model of coupled Whitham-Broer-Kaup equation by Jagdev Singh, Arpita Gupta, Dumitru Baleanu

“…In this research paper, we study a semi analytical technique to solve the nonlinear partial differential equations. This technique is good combination of homotopy analysis method with Kharrat-Toma transform. …”
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Optimal control of agent-based models via surrogate modeling. by Luis L Fonseca, Lucas Böttcher, Borna Mehrad, Reinhard C Laubenbacher

“…For a given ABM and a given optimal control problem, the algorithm derives a surrogate model, typically lower-dimensional, in the form of a system of ordinary differential equations (ODEs), solves the control problem for the surrogate model, and then transfers the solution back to the original ABM. …”
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DYNAMIC ANALYSIS OF 6-TPS PARALLEL MECHANISM by GAO XiuLan, ZHANG MinYing, ZHANG FengTao, SHI GeMeng, LU KaiJiang

“…The mechanism output speed is used as the independent variable,and set up the mechanism motion differential equations by Kane method. The equation can be used as a dynamic control model and be completely closed loop control of the mechanism. …”
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The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes by Peng Li, Chuancun Yin, Ming Zhou

“…Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. …”
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Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy by Chao Yue, Tiecheng Xia

“…Then, the CCIRD equations are decomposed into Dubrovin-type ordinary differential equations. Furthermore, the theory of the trigonal curve and the properties of the three kinds of Abel differentials are applied to obtain the explicit theta function representations of the Baker-Akhiezer function and the meromorphic functions. …”
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T model of growth and its application in systems of tumor-immunedynamics by Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae

“…We recommend usage of the T growth model forthe growth of tumors as part of any system of differential equations. Use ofthis model within a system will allow more flexibility in representing thenatural rate of tumor growth. …”
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On Modeling and Constrained Model Predictive Control of Open Irrigation Canals by Lihui Cen, Ziqiang Wu, Xiaofang Chen, Yanggui Zou, Shaohui Zhang

“…As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. …”
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Computer-Aided Numerical Inversion of Laplace Transform by Umesh Kumar

“…This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.…”
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