A Jacobi Collocation Method for Solving Nonlinear Burgers-Type Equations by E. H. Doha, D. Baleanu, A. H. Bhrawy, M. A. Abdelkawy

“…Also the results demonstrate that the proposed method is a powerful algorithm to solve the nonlinear partial differential equations.…”
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Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics by Fazle Mabood, Nopparat Pochai, Stanford Shateyi

“…The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. …”
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Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption by Kh. Abdul Maleque

“…Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. …”
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SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects by Tongqian Zhang, Xinzhu Meng, Tonghua Zhang

“…We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. …”
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Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops by F. Moriello

“…This is achieved by defining differential equations along contours connecting two fixed points, and by solving them in terms of one-dimensional generalised power series. …”
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Analysis of Metallic Nanoparticles (Cu, Al2O3, and SWCNTs) on Magnetohydrodynamics Water-Based Nanofluid through a Porous Medium by P. K. Pattnaik, S. K. Parida, S. R. Mishra, M. Ali Abbas, M. M. Bhatti

“…To formulate the mathematical modelling, similarity transformations were used, and nonlinear differential equations were obtained. To solve the formulated nonlinear differential equations, the Runge–Kutta fourth-order numerical scheme is used in conjunction with the shooting technique. …”
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The Effects of MHD Flow and Heat Transfer for the UCM Fluid over a Stretching Surface in Presence of Thermal Radiation by M. Subhas Abel, Jagadish V. Tawade, Jyoti N. Shinde

“…The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. …”
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Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations by S. M. Sayed, A. S. Mohamed, E. M. Abo-Eldahab, Y. H. Youssri

“…The current algorithm is simple to set up and is better suited to solving certain difficult partial differential equations.…”
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A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. …”
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Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate by Shuang Li, Shican Liu, Yanli Zhou, Yonghong Wu, Xiangyu Ge

“…By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. …”
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Sliding Mode Output Feedback Control of a Flexible Rotor Supported by Magnetic Bearings by A. S. Lewis, A. Sinha, K. W. Wang

“…A mathematical model of the rotor]magnetic bearing system is presented in terms of partial differential equations. These equations are then discretized into a finite number of ordinary differential equations through Galerkin’s method. …”
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Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency by Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, Richard Guiem

“…The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. …”
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Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects by Faisal Salah

“…This contrast is important because it shows how precisely the successive linearization method can resolve a set of nonlinear differential equations. Following that, the generated solution is studied and explained in relation to a variety of engineering parameters. …”
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DC Glow Discharge in Axial Magnetic Field at Low Pressures by Shen Gao, Shixiu Chen, Zengchao Ji, Wei Tian, Jun Chen

“…Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. …”
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Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate by Winifred Nduku Mutuku-Njane, Oluwole Daniel Makinde

“…A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. …”
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Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks by Van Truong Vo, Samad Noeiaghdam, Denis Sidorov, Aliona Dreglea, Liguo Wang

“…Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. …”
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Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect by Alharbi Abdulaziz H.

“…H2O{\text{H}}_{\text{2}}\text{O}) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. …”
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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. …”
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Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters by M. M. Rashidi, E. Momoniat, B. Rostami

“…The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). …”
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Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System by Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, Valery Stolbov

“…Results on nonnegativity of the Cauchy matrix for system of delay differential equations xi′t+∑j=1n‍pijtxjhijt=fit,   i=1,…,n, which were based on nonpositivity of all diagonal elements, were presented in the previous works. …”
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