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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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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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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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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Dynamics of a delay Schistosomiasis model in snail infections by Chunhua Shan, Hongjun Gao, Huaiping Zhu

“…In this paper we modify and study a system of delay differential equations model proposed by Nåsell and Hirsch (1973) for the transmission dynamics of schistosomiasis. …”
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Global Stability of HIV-1 Infection Model with Two Time Delays by Hui Miao, Xamxinur Abdurahman, Ahmadjan Muhammadhaji

“…We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. …”
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Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. …”
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Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order by A. Kazemi Nasab, A. Kılıçman, Z. Pashazadeh Atabakan, S. Abbasbandy

“…A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. …”
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Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations by Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam

“…With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. …”
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Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method by Shao-Hong Yan, Xiao-Hong Chen, Gong-Nan Xie, Carlo Cattani, Xiao-Jun Yang

“…The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.…”
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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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