Efficient numerical technique for solution of delay Volterra-Fredholm integral equations using Haar wavelet

• Published in: Heliyon Vol. 6; no. 10; p. e05108
• Main Authors: Amin, Rohul, Shah, Kamal, Asif, Muhammad, Khan, Imran
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2020; Elsevier
• Subjects: Collocation method; Delay Fredholm integral equations; Delay Volterra integral equations; Haar wavelet; Integral equations; Mathematics; Mathematics; Delay Fredholm integral equations; Delay Volterra integral equations; Collocation method; Integral equations; Haar wavelet
• ISSN: 2405-8440; 2405-8440
• DOI: 10.1016/j.heliyon.2020.e05108

In this article, a computational Haar wavelet collocation technique is developed for the solution of linear delay integral equations. These equations include delay Fredholm, Volterra and Volterra-Fredholm integral equations. First we transform the derived estimates for these equations. After that, we transform these estimates to a system of algebraic equations. Finally, we solve the obtained algebraic system by Gauss elimination technique. Numerical examples are taken from literature for checking the validity and convergence of the proposed technique. The maximum absolute and root mean square errors are compared with the exact solution. The convergence rate using distinct numbers of collocation points is also calculated, which is approximately equal to 2. All algorithms for the developed method are implemented in MATLAB (R2009b) software. Mathematics; Integral equations; Delay Volterra integral equations; Delay Fredholm integral equations; Haar wavelet; Collocation method