On Taylor-series expansion methods for the second kind integral equations
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/29329 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Mahidol University |
| Summary: | 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. © 2010 Elsevier B.V. All rights reserved. |
|---|