Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations
Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations
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一般线性 Fredholm 积分微分方程解的勒让德多项式近似与变分迭代法的比较
DOI：
10.1016/j.camwa.2009.06.022
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Yalçınbaş
中科院分区：
文献类型：
--
作者：
N. Bildik;A. Konuralp;S. Yalçınbaş
本文证明了用勒让德多项式得到的线性Fredholm积分微分方程的数值解也可以用变分迭代法求出。用变分迭代法求解问题的数值解，明显比用勒让德多项式法更快地收敛到精确解。另外，虽然勒让德多项式方法中的应用过程在初始函数逼近值未知的情况下会产生强大的影响，但通过实例表明，在第一初始函数逼近值被估计的情况下，变分迭代法产生更确定的解。本文分别用勒让德多项式逼近法（LPA）和变分迭代法（Vim）求解线性Fredholm积分微分方程，并对这两种方法的数值解进行了比较。
In this study it is shown that the numerical solutions of linear Fredholm integro-differential equations obtained by using Legendre polynomials can also be found by using the variational iteration method. Furthermore the numerical solutions of the given problems which are solved by the variational iteration method obviously converge rapidly to exact solutions better than the Legendre polynomial technique. Additionally, although the powerful effect of the applied processes in Legendre polynomial approach arises in the situations where the initial approximation value is unknown, it is shown by the examples that the variational iteration method produces more certain solutions where the first initial function approximation value is estimated. In this paper, the Legendre polynomial approximation (LPA) and the variational iteration method (VIM) are implemented to obtain the solutions of the linear Fredholm integro-differential equations and the numerical solutions with respect to these methods are compared.