Numerical solution of integral equations by means of the Sinc collocation method based on the double exponential transformation
Numerical solution of integral equations by means of the Sinc collocation method based on the double exponential transformation
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DOI：
10.1016/j.cam.2004.09.019
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发表时间：
2005-05
影响因子：
2.4
通讯作者：
M. Muhammad;Ahniyaz Nurmuhammad;M. Mori;M. Sugihara
中科院分区：
文献类型：
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作者：
M. Muhammad;Ahniyaz Nurmuhammad;M. Mori;M. Sugihara
考虑了用基于双指数变换的SINC配置法(简称DE变换)数值解线性积分方程组。我们首先将该方法应用于第二类Volterra积分方程，然后再应用于第一类Volterra方程。该方法也适用于第二类Fredholm型积分方程解。对于Volterra方程，我们采用了Muhammad和Mori发展的数值不定积分公式，该公式是通过将DE变换结合到被积函数的SINC展开中而得到的，而对于Fredholm方程，我们对定积分采用了传统的DE变换。给出了该方法的误差分析，并在每种情况下建立了误差的收敛速度O(exp(-cn/logn))，其中N是表示sinc展开的项数的参数。此外，通过对程序返回的条件数的估计来观察主线性方程组的矩阵的条件。数值算例表明了该方法的收敛速度，验证了该方法的高效性。
Numerical solution of linear integral equations by means of the Sinc collocation method based on the double exponential transformation, abbreviated the DE transformation, is considered. We first apply the method to the Volterra integral equation of the second kind and then to the Volterra equation of the first kind. This method is also applied to the Fredholm integral equation of the second kind. For the Volterra equations we employed a formula for numerical indefinite integration developed by Muhammad and Mori obtained by applying the DE transformation incorporated into the Sinc expansion of the integrand, while for the Fredholm equation we employed the conventional DE transformation for definite integrals. An error analysis of the method is given and in every case a convergence rate of O(exp(-cN/logN)) for the error is established where N is a parameter representing the number of terms of the Sinc expansion. Also, the condition of the matrix of the main system of linear equations is watched through an estimate of the condition number returned by the program. Numerical examples show the convergence rate mentioned above and confirm the high efficiency of the present method.