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An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method

机译：用改进的微分变换方法解决一类非线性奇异边值问题的有效数值方法

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1. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
2. A quasilinearization method for a class of second order singular nonlinear differential equations with nonlinear boundary conditions [J] . El-Gebeily M, ORegan D Nonlinear analysis. Real world applications . 2007,第1期

机译：一类具有非线性边界条件的二阶奇异非线性微分方程的拟线性化方法
3. A class of numerical methods for the solution of fourth-order nonlinear ordinary differential equations on a graded mesh with boundary conditions of first kind [J] . International Journal for Computational Methods in Engineering Science and Mechanics . 2019,第1a6期

机译：一种具有第一类边界条件的分级网上四阶非线性常微分方程解决的一类数值方法
4. Application of Differential Transform Method and Adomian Decomposition Method for Solving of one Nonlinear Boundary-Value-Transmission Problem [C] . Merve YüCEL, Oktay MUKHTAROV International Conference of Mathematical Sciences . 2019

机译：差分变换法和ADOMIAN分解方法解决一个非线性边界值传输问题的应用
5. Meshless Methods for Numerically Solving Boundary Value Problems of Elliptic Type Partial Differential Equations [D] . Choi, Minhwa 2018

机译：数值求解椭圆型偏微分方程边值问题的无网格方法
6. An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method [O] . Lie-jun Xie, Cai-lian Zhou, Song Xu -1

机译：用改进的微分变换方法解决一类非线性奇异边值问题的有效数值方法
7. An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method [O] . Xie, Lie-jun, Zhou, Cai-lian, Xu, Song 2016

机译：求解一类非线性奇异系统的有效数值方法利用改进的微分变换方法研究边值问题

An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method

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