Pallop HuabsomboonBoriboon NovaprateepHideaki KanekoMahidol UniversityOld Dominion University2018-09-242018-09-242010-07-01Journal of Computational and Applied Mathematics. Vol.234, No.5 (2010), 1466-1472037704272-s2.0-77950790792https://repository.li.mahidol.ac.th/handle/20.500.14594/29329In 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. © 2010 Elsevier B.V. All rights reserved.Mahidol UniversityMathematicsArticleSCOPUS10.1016/j.cam.2010.02.023