An Analytical Study on Two High-Order Hybrid Methods to Solve Systems of Nonlinear Equations by Hooman Darvishi, M. T. Darvishi

“…These algorithms are applied for solving two real stiff systems of ordinary differential equations. These systems arise from an HIV spreading model and an SIR model of an epidemic which formulates the spread of a nonfatal disease in a certain population. …”
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Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey–Stewartson System by Tianyong Han, Jiajin Wen, Zhao Li

“…By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. …”
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Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations by Azam Zahrani, Mashaallah Matinfar, Mostafa Eslami

“…This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. …”
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Epidemic Analysis and Mathematical Modelling of Influenza with Vaccination. by Musiime, Catherine

“…In this study, we discuss a SLIRV model developed by Jonnalagadda & Gaddam (2016) for the transmission of influenza A with vaccination using tools from ordinary differential equations. We show that if the product of the recruitment rate and the ratio of infection rate to mean latent period is less than the product the sums µ + m, µ + m and + a + y; where µ, a, y, m and 1/ware natural death rate, disease-related death rate, recovery rate, vaccination rate and mean latent period, respectively; then the disease-free equilibrium will be locally and globally asymptotically stable, an indication that that disease can be eradicated from the population.…”
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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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Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems by Hassan Saberi Nik, Paulo Rebelo

“…The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. …”
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A singular limit for an age structured mutation problem by Jacek Banasiak, Aleksandra Falkiewicz

“…The spread of a particular trait in a cell population often is modelled by an appropriate system of ordinary differential equations describing how the sizes of subpopulations of the cells with the same genome change in time. …”
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On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes by Pramod Pandey

“… In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. …”
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The numerical models of the estimation of the electrooptical parameters of GaAs by Albertas Pincevičius, Rimantas-Jonas Rakauskas, Svajonė Vošterienė

“…The system of the differential equations was solved by a method Gear with a modification of a step. …”
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Abundant Interaction Solutions of Sine-Gordon Equation by DaZhao Lü, YanYing Cui, ChangHe Liu, ShangWen Wu

“…The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. …”
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Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane by H. K. Mondal, T. K. Chaudhury

“…Velocity distribution is also obtained for certain values of the parameters by integrating the coupled differential equations by Runge-Kutta method and compared with the analytical solution. …”
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A Fixed Point Technique for Set-Valued Contractions with Supportive Applications by Hasanen A. Hammad, Manuel De la Sen

“…Finally, the theoretical results are used to study the existence of the solution of Fredholm integral equation which arises from the damped harmonic oscillator, to study initial value problem which arises from Newton’s law of cooling and to study infinite systems of fractional ordinary differential equations (ODEs).…”
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Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays by Huitao Zhao, Yiping Lin, Yunxian Dai

“…Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. …”
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Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates by Ya-Juan Hao, H. M. Srivastava, Hossein Jafari, Xiao-Jun Yang

“…The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.…”
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Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem by R. J. Moitsheki, M. D. Mhlongo

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A mathematical model of stem cell regeneration with epigenetic state transitions by Qiaojun Situ, Jinzhi Lei

“…The dynamics of the subpopulations are modeled by a set of ordinary differential equations in which epigenetic state transition in cell division is given by the transition probability. …”
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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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Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel by Jawad Raza, Azizah Mohd Rohni, Zurni Omar

“…Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. …”
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Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method by Berna Bülbül, Mehmet Sezer

“…We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. …”
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Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay by Lixia Zuo, Maoxing Liu

“…The model is analyzed by using stability theory of differential equations and numerical simulations. Both equilibria have been proved to be globally asymptotically stable. …”
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