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

Abstract

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.

Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations

“…The works by Amin et al [35] , [36] , [37] , [38] , and [39] contribute to the development of efficient algorithms and numerical techniques for fractional integro-differential equations and delay Volterra-Fredholm integral equations. They explore the applications of Haar wavelets and other methods in solving these equations and discuss the advantages and effectiveness of the proposed approaches.…”

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

“…Jonathan Lenells provided foundation for the geometric study of HS equation, this exhibits a geodesic flow. The system of nonlinear DEs like Hunter-Saxton, Camassa-Holm and Degasperis-Procesi was analyzed by variational principle to find the weak solutions in [8] , Volterra-Fredholm integral equations [9] , Boussinesq equations [10] , Schrödinger equation [11] , [12] , telegraph PDEs [13] , [14] , Burgers equation [15] . There are several researches in the literature, that are examined by the different techniques [16] , [17] , [18] , [19] , [20] .…”

Numerical Investigation of Fractional-Order Differential Equations via φ -Haar-Wavelet Method

“…It also includes the lower member of the Daubechies wavelet family, which is suitable for computer implementation. The Haarwavelets are used to transform a fractional differential equation into an algebraic structure of finite variables [24][25][26][27].…”