N-变换在求解偏微分方程中的应用

Applications of the Natural Transform for Solving PDEs

本文研究N-变换在偏微分方程中的应用.N-变换是一种新的积分变换,它类似于Lapalace变换和Sumudu变换.通过改变变量,该变换可以收敛到Lapalace变换和Sumudu变换.该方法非常有效、简单,可用于其它非线性问题的求解.利用该方法得到了半有界杆的热传导方程和粘性伯格斯方程的初值问题的精确解.计算结果与现有的其他方法得到的结果是一致的.结果表明N-变换是简单有效的.

In this paper we consider the applications of the Natural transform in partial differential equations.The Natural transform is a new integral transform which is similar to the Lapalace transform and Sumudu transform.By changing variables,this transform can converge to Laplace transform and sumudu transform.This method is very effective and simple,and can be used to solve other nonlinear problems.By using the proposed method,exact solutions of the heat conduction equation for semi-bounded bar and the initial value problem for the viscid Burgers equation are obtained.The results are consistent with the existing ones obtained by other methods.It is shown that the Natural transform is simple and effective.