The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations
Abdou, M., Elhamaky, M., Soliman, A., Mosa, G. (2020). The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations. EKB Journal Management System, 5(Issue 7 part (1) - (2)), 189-198. doi: 10.21608/bjas.2020.226978
M.A. Abdou; M.N. Elhamaky; A.A. Soliman; G.A. Mosa. "The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations". EKB Journal Management System, 5, Issue 7 part (1) - (2), 2020, 189-198. doi: 10.21608/bjas.2020.226978
Abdou, M., Elhamaky, M., Soliman, A., Mosa, G. (2020). 'The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations', EKB Journal Management System, 5(Issue 7 part (1) - (2)), pp. 189-198. doi: 10.21608/bjas.2020.226978
Abdou, M., Elhamaky, M., Soliman, A., Mosa, G. The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations. EKB Journal Management System, 2020; 5(Issue 7 part (1) - (2)): 189-198. doi: 10.21608/bjas.2020.226978

The Error Behaviour of Collocation and Galerkin Methods in Solving Integral Equations

Benha Journal of Applied Sciences
Article 31, Volume 5, Issue 7 part (1) - (2), October 2020, Page 189-198  XML PDF (1.61 MB)
Document Type: Original Research Papers
DOI: 10.21608/bjas.2020.226978
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Authors
M.A. Abdou1; M.N. Elhamaky2; A.A. Soliman2; G.A. Mosa2
1Mathematics Dept., Faculty of Education, Alexandria Univ., Benha, Egypt
2Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt
Abstract
This paper was devoted to study the error behaviour of the solutions for Fredholm and Volterra integral equations of the second
kind using Collocation and Galerkin methods at N=3:100. This paper started with an introduction to show the related work. In
addition, we presented the analysis of the numerical methods which we used. Under certain conditions, Banach’s fixed point theorem
was used to prove the existence and uniqueness for the error integral equation. We presented a comparison between the maximum
and minimum errors obtained by Collocation and Galerkin methods. Moreover, some applications were given to satisfy our study.
Results were represented in groups of tables and figures.
Keywords
Integral Equations (IEs); Collocation method (CM); Galerkin method (GM); Behaviour of error
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