On Taylor-series expansion methods for the second kind integral equations

• Published in: Journal of computational and applied mathematics 2010-07, Vol.234 (5), p.1466-1472
• Main Authors: Huabsomboon, Pallop, Novaprateep, Boriboon, Kaneko, Hideaki
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fredholm integral equation; Functions of a complex variable; Integral equations; Mathematical analysis; Mathematics; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; System of integral equations; Taylor method
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2010.02.023

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.