Analytical and numerical solutions for the current and voltage model on an electrical transmission line with time and distance
Analytical and numerical solutions for the current and voltage model on an electrical transmission line with time and distance
复制标题
DOI：
10.1088/1402-4896/ab61dd
复制
发表时间：
2020-02
期刊：
影响因子：
2.9
通讯作者：
Mostafa M. A. Khater;J. F. Alzaidi;R. Attia;M. Inc.;D. Lu
中科院分区：
文献类型：
--
作者：
Mostafa M. A. Khater;J. F. Alzaidi;R. Attia;M. Inc.;D. Lu
本文采用三种不同的方法对分数阶非线性时空电报方程进行求解，得到了孤立波解、半解析解和数值解。我们在分数电报方程上实现了修改的Khater方法、Adomian分解方法和B样条技术（三次、四次和分解）。该模型是电传输和电磁波中的基本方程之一，其描述电传输线上的电流和电压随时间和距离的变化。它是由奥利弗·赫维赛德在19世纪80年代提出的，用来讨论电磁波通过沿着直线时的镜像现象和波型。得到了孤立波行波解的新的结构形式，并对这三种解进行了比较。用Maple 16和Mathematica 12验证了所得到的解，并将其放回原始方程中。这些方法的性能表明，他们的权力和有效性，适用于许多不同形式的非线性偏微分方程的整数阶和分数阶。
This research paper employs three different techniques on the fractional nonlinear space-time telegraph equation to get the solitary traveling wave solutions, semi-analytical wave solution, and numerical solutions. We implement a modified Khater method, Adomian decomposition method, and B-spline techniques (cubic, quantic, and septic) on the fractional telegraph equation. This model is one of the fundamental equations in an electrical transmission and electromagnetic waves that describes the current and voltage on an electrical transmission line with time and distance. It derived by Oliver Heaviside in the 1880s and used to discuss the mirror phenomena of the electromagnetic waves and wave patterns through along line. New structure forms of solitary traveling wave solutions are obtained, and the comparison between the three kinds of solutions is given. The obtained solutions verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows the power and effectiveness of them for applying to many different forms of the nonlinear partial differential equation with integer order and fractional order.