Product Block for Volterra Integral Equations of the Second Kind with Singular Kernel.

Authors

Salah El-Emam, Mechanical Power Engineering Department., Faculty of Engineering., El-Mansoura University., Mansoura., Egypt.Follow
G. Attia, Mathematics & Physics Engineering Department., Faculty of Engineering., El-Mansoura University., Mansoura., Egypt.
A. Hussean, Mathematics & Physics Engineering Department., Faculty of Engineering., Cairo University., Cairo., Egypt.
S. El-Kotb, Mathematics & Physics Engineering Department., Faculty of Engineering., El-Mansoura University., Mansoura., Egypt.

Corresponding Author

El-Kotb, S.

Subject Area

Mathematics and Engineering Physics

Article Type

Original Study

Abstract

The block method is a good self-starting method for solving volterra integral equations with continuous kernel. In this paper two modifications are suggested to develop block method and to use it to solve volterra integral equations of the second kind with singular kernel . The idea of the product technique is used for block method, which is the first modification, while the second modification is the use of the graded nodes with block method. Some algorithms are considered and the solution procedures are carried out. Implementation and testing of the considered algorithms have been done. The results show that the graded nodes give good results compared with equal spaced nodes.

Recommended Citation

El-Emam, Salah; Attia, G.; Hussean, A.; and El-Kotb, S. (2020) "Product Block for Volterra Integral Equations of the Second Kind with Singular Kernel.," Mansoura Engineering Journal: Vol. 23 : Iss. 2 , Article 6.
Available at: https://doi.org/10.21608/bfemu.2021.149968