Superconvergence of the iterated Galerkin methods for Hammerstein equations
SIAM Journal on Numerical Analysis
A simple Taylor-series expansion method for a class of second kind integral equations
Journal of Computational and Applied Mathematics
On Taylor-series expansion methods for the second kind integral equations
Journal of Computational and Applied Mathematics
On Taylor-series expansion methods for the second kind integral equations
Journal of Computational and Applied Mathematics
A modified Taylor series method to the classical Love's equation
ACC'11/MMACTEE'11 Proceedings of the 13th IASME/WSEAS international conference on Mathematical Methods and Computational Techniques in Electrical Engineering conference on Applied Computing
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In this paper, we comment on the recent papers by Yuhe Ren et al. (1999) [1] and Maleknejad et al. (2006) [7] concerning the use of the Taylor series to approximate a solution of the Fredholm integral equation of the second kind as well as a solution of a system of Fredholm equations. The technique presented in Yuhe Ren et al. (1999) [1] takes advantage of a rapidly decaying convolution kernel k(|s-t|) as |s-t| increases. However, it does not apply to equations having other types of kernels. We present in this paper a more general Taylor expansion method which can be applied to approximate a solution of the Fredholm equation having a smooth kernel. Also, it is shown that when the new method is applied to the Fredholm equation with a rapidly decaying kernel, it provides more accurate results than the method in Yuhe Ren et al. (1999) [1]. We also discuss an application of the new Taylor-series method to a system of Fredholm integral equations of the second kind.