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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Higher-Order Compact Finite Difference for Certain PDEs in Arbitrary Dimensions by Yan Gao, Songlin Liu

“…In addition, a fine description of the sixth-order CFD schemes is also developed for equations with constant coefficients, which is used to discuss certain partial differential equations (PDEs) with arbitrary dimensions. In this paper, various ways of numerical test calculations are prepared to evaluate performance of the fourth-order CFD and sixth-order CFD schemes, respectively, and the empirical results are proved to verify the effectiveness of the schemes in this paper.…”
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Mode Transition Phenomenon of Herringbone Gear Power-split Transmission System by Jincheng Dong, Sanmin Wang

“…The torsional vibration model and the free torsional vibration differential equations of the herringbone gear power-split transmission system are established， and the torsional vibration models are classified to two kinds of the coupled vibration mode and the branch gear vibration model by calculating the torsional vibration natural frequency and vibration mode. …”
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Valuation of Credit Derivatives with Multiple Time Scales in the Intensity Model by Beom Jin Kim, Chan Yeol Park, Yong-Ki Ma

“…We propose approximate solutions for pricing zero-coupon defaultable bonds, credit default swap rates, and bond options based on the averaging principle of stochastic differential equations. We consider the intensity-based defaultable bond, where the volatility of the default intensity is driven by multiple time scales. …”
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Optical vortices in dispersive nonlinear Kerr-type media by Lubomir M. Kovachev

“…The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. …”
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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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Dynamic Analysis on a Diffusive Two-Enterprise Interaction Model with Two Delays by Yanxia Zhang, Long Li

“…In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. Finally, numerical simulation experiments are conducted to illustrate the validity of the theoretical conclusions.…”
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Convergence in Distribution of Some Self-Interacting Diffusions by Aline Kurtzmann

“…These diffusions are solutions to stochastic differential equations: dXt=dBt-g(t)∇V(Xt-μ¯t)dt, where μ¯t is the empirical mean of the process X, V is an asymptotically strictly convex potential, and g is a given positive function. …”
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Computational modeling approaches to studying the dynamics of oncolytic viruses by Dominik Wodarz

“…This article reviews different mathematical modelingapproaches ranging from ordinary differential equations to spatiallyexplicit agent-based models. …”
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Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion by Di Pan, Shengwu Zhou, Yan Zhang, Miao Han

“…The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. …”
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A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems by A. H. Bhrawy, M. A. Alghamdi

“…We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. …”
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The Investigation of MHD Williamson Nanofluid over Stretching Cylinder with the Effect of Activation Energy by Wubshet Ibrahim, Mekonnen Negera

“…Dimensionless ordinary differential equations are obtained from the modeled PDEs by using appropriate transformations. …”
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Epidemic models with differential susceptibility and stagedprogression and their dynamics by James M. Hyman, Jia Li

“…We formulate and study epidemic models with differential susceptibilities andstaged-progressions, based on systems of ordinary differential equations, fordisease transmission where the susceptibility of susceptible individuals varyand the infective individuals progress the disease gradually through stageswith different infectiousness in each stage. …”
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Explicit Solutions of a Gravity-Induced Film Flow along a Convectively Heated Vertical Wall by Ammarah Raees, Hang Xu

“…The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). …”
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An Improved Version of Residual Power Series Method for Space-Time Fractional Problems by Mine Aylin Bayrak, Ali Demir, Ebru Ozbilge

“…The parameter λ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. …”
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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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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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