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, Pages 189-198 PDF (1.61 M) | ||
| Document Type: Original Research Papers | ||
| DOI: 10.21608/bjas.2020.226978 | ||
| 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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