Amin Rohul, Shah Kamal, Asif Muhammad, Khan Imran
Department of Mathematics, University of Peshawar, Peshawar, 25120, Khyber Pakhtunkhwa, Pakistan.
Department of Mathematics, University of Malakand, Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan.
Heliyon. 2020 Oct 6;6(10):e05108. doi: 10.1016/j.heliyon.2020.e05108. eCollection 2020 Oct.
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.
在本文中，为求解线性延迟积分方程开发了一种计算哈尔小波配置技术。这些方程包括延迟弗雷德霍姆积分方程、沃尔泰拉积分方程和沃尔泰拉 - 弗雷德霍姆积分方程。首先，我们对这些方程的推导估计进行变换。之后，我们将这些估计变换为代数方程组。最后，我们通过高斯消元技术求解得到的代数系统。从文献中选取数值例子来检验所提出技术的有效性和收敛性。将最大绝对误差和均方根误差与精确解进行比较。还计算了使用不同数量配置点时的收敛速率，其近似等于2。所开发方法的所有算法都在MATLAB（R2009b）软件中实现。
