Comparing Linear and Nonlinear Differential Equations of Differential Transformation Method by Other Numerical Methods

机译：用其他数值方法比较差分变换方法的线性和非线性微分方程

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In this study, we solve fifth-order boundary value problems by using the DTM for linear and nonlinear differential equations and compare the results with other methods such as Adomian Decomposition Method (ADM), Noor Decomposition Method and Variational Iteration Method. We provide several numerical examples in order to show the accuracy of the method. Further, we also solve sixth-order nonlinear boundary value problems and compare the result to ADM. The present study shows that the DTM is able to provide good results with high accuracy and the method is also easy to apply.

机译：在这项研究中，我们通过使用DTM用于线性和非线性微分方程来解决第五阶边值问题，并将结果与其他方法进行比较，例如Adomian分解方法（ADM），NOOR分解方法和变分迭代方法。我们提供了几个数值例子，以显示方法的准确性。此外，我们还解决了第六阶非线性边值问题并将结果与ADM进行比较。本研究表明，DTM能够高精度提供良好的结果，并且该方法也很容易涂抹。

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《International Conference on Mathematical Sciences》|2014年||共7页
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Che Haziqah Che Hussin; Adem Kilicman; Arif Mandangan;
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中图分类 O1-532;
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Ordinary Differential Equations; Numerical approximation and analysis;

机译：常微分方程;数值近似和分析;

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1. Discussion on ????????Numerical solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics????????, ????????Analogue solution of 2nd-order hyperbolic partial differential equations by the method of continuous characteristics???????? and ????????Analogue solution of elliptic differential equations by conformal transformations???????? [J] . Electrical Engineers, Proceedings of the Institution of . 1971,第6期

机译：用连续特性方法讨论二阶双曲型偏微分方程的数值解??????，二阶双曲型的模拟解偏微分方程的连续特性方法和利用共形变换的椭圆型微分方程的模拟解
2. Numerical methods for nonlinear second-order hyperbolic partial differential equations. I. Time-linearized finite difference methods for 1-D problems [J] . Ramos JI Applied mathematics and computation . 2007,第1期

机译：非线性二阶双曲型偏微分方程的数值方法。 I.一维问题的时间线性化有限差分方法
3. Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation [J] . Abbasbandy S, Taati A Journal of Computational and Applied Mathematics . 2009,第1期

机译：具运算Tau法和误差估计的具有非线性微分部分的非线性Volterra积分-微分方程组的数值解
4. Comparing Linear and Nonlinear Differential Equations of Differential Transformation Method by Other Numerical Methods [C] . Che Haziqah Che Hussin, Adem Kilicman, Arif Mandangan International Conference on Mathematical Sciences . 2014

机译：用其他数值方法比较差分变换方法的线性和非线性微分方程
5. Numerical methods for nonlinear partial differential equations of Gross-Pitaevskii type and their discrete analogues. [D] . Savytska, Nataliya Y. 2002

机译：Gross-Pitaevskii型非线性偏微分方程及其离散类似物的数值方法。
6. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things [O] . Rohul Amin, Shah Nazir, Iván García-Magariño 2020

机译：无线传感器网络与物联网非线性时滞积分微分方程数值解的配置方法
7. Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation [O] . Abbasbandy S., Taati A. 2009

机译：运用运算Tau法和误差估计的带有非线性微分部分的非线性Volterra积分-微分方程组的数值解
8. Nonlinear Problems and Numerical Methods in Differential Equations and AppliedPhenomena [R] . Cohen, D. S. 1993

机译：微分方程的非线性问题和数值方法及应用现象

Comparing Linear and Nonlinear Differential Equations of Differential Transformation Method by Other Numerical Methods

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