Error Analysis of Galerkin's Method for Semilinear Equations by Tadashi Kawanago

“…Some of our results may be applicable for investigating the quality of numerical verification methods for solutions of ordinary and partial differential equations.…”
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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation by Hassan Eltayeb, Said Mesloub

“…It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. …”
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Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects by Jia-Fang Zhang

“…Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs).…”
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A Mathematical Model for the Dynamics of Income Distribution in the Presence of Production by Maria Letizia Bertotti

“…The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. …”
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Calculation of Wall Heat Conductivity under Non-Symmetric Boundary Conditions by R. I. Yesman

“…Advancing of phase transformation front along cross-section is considered with the purpose to take into account phase and chemical transformations in high-impact coatings and the Dirac δ-function is applied in this case.While stating a problem nonlinear boundary conditions and differential equations of heat transfer with due account of thermal and physical characteristics dependence on temperature have been used in the paper. …”
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Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form by Imre F. Barna, Mihály A. Pocsai, L. Mátyás

“…The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.…”
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A New Fractional Representation of the Higher Order Taylor Scheme by Iqbal M. Batiha, Iqbal H. Jebril, Amira Abdelnebi, Zoubir Dahmani, Shawkat Alkhazaleh, Nidal Anakira

“…In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor’s theorem is the fundamental concept of this approach. …”
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New Results for Multipoint Singular Boundary Value Problems on a Measure Chain by Yan Sun, Yongping Sun, Patricia J. Y. Wong

“…We study the existence and uniqueness of positive solutions for a class of singular m-point boundary value problems of second order differential equations on a measure chain. A sharper sufficient condition for the existence and uniqueness of Crd⁡1[0,T] positive solutions as well as Crd⁡1[0,T] positive solutions is obtained by the technique of lower and upper solutions and the maximal principle theorem.…”
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Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations by Rodica D. Costin, Marina David

“…As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in C.…”
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Convergence of the solutions for the equation x(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛) by Anthony Uyi Afuwape

“…This paper is concerned with differential equations of the formx(iv)+ax ⃛+bx¨+g(x˙)+h(x)=p(t,x,x˙,x¨,x ⃛)where a, b are positive constants and the functions g, h and p are continuous in their respective arguments, with the function h not necessarily differentiable. …”
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New Neumann System Associated with a 3 × 3 Matrix Spectral Problem by Fang Li, Liping Lu

“…As an application, solutions of the first nontrivial equation related to the 3 × 3 matrix spectral problem are decomposed into solving two compatible Hamiltonian systems of ordinary differential equations.…”
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Convexity of the Set of Fixed Points Generated by Some Control Systems by Vadim Azhmyakov

“…We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs) and establish convexity of the set of trajectories. …”
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Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow by Yang Li, Long-Fei Wang, Sheng-Da Zeng, Yang Zhao

“…We discuss the line partial differential equations arising in fractal vehicular traffic flow. …”
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Three-loop ladder diagrams with two off-shell legs by Ming-Ming Long

“…We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical regions. …”
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Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation by Mostafa Abbaszadeh, Mehdi Dehghan, Mahmoud A. Zaky, Ahmed S. Hendy

“…A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. …”
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A Generalized Approach of Triple Integral Transforms and Applications by Rania Saadeh

“…We apply the general triple transform to solve some applications of various types of partial differential equations. The strength of the new approach is that it covers almost all integral transforms of order one, two, and three, and hence no need to find new formulas of triple integral transforms or to study the basic properties.…”
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Analytical Approximate Solution of Chemical Kinetics Problems by Hatıra Günerhan

“…Proposed problem is system of nonlinear ordinary differential equations. We show converges analysis of the differential transform method. …”
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Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers by Xiaoyu Jiang, Kicheon Hong

“…Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. …”
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Positive Solutions of a General Discrete Dirichlet Boundary Value Problem by Xinfu Li, Guang Zhang

“…To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different.…”
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Multivalued Impulsive SDEs Driven by G-Brownian Noise: Periodic Averaging Result by Mahmoud Abouagwa, Anas D. Khalaf, Nadia Gul, Sultan Alyobi, Al-Sharef Mohamed

“…This paper aims to study two approximation theorems in view of the periodic averaging results for non-Lipschitz multivalued stochastic differential equations with impulses and G-Brownian motion (MISDEGs). …”
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