Abstract
In this work, the Haar collocation scheme is used for the solution of the class of system of delay integral equations for heterogeneous data communication. The Haar functions are considered for the approximation of unknown function. By substituting collocation points and applying the Haar collocation technique to system of delay integral equations, we have obtained a linear system of equations. For the solution of this system, an algorithm is developed in MATLAB software. The method of Gauss elimination is utilized for the solution of this system. Finally, by using these coefficients, the solution at collocation points is obtained. The convergence of Haar technique is checked on some test problems.
Highlights
Integral equations (IEs) are equations in which the unknown functions appear under one or more integral signs [1]
Delay integral equations (DIEs) are those IEs in which the solution of the unknown function is given in the previous time interval [2]
A Volterra-Fredhom DIEs consist of disjoint Volterra and Fredhom IEs [1]. e DIEs play an important role in mathematics [3]. ese equations are used for modelling of various phenomena such as modelling of systems with memory [4], mathematical modelling, electric circuits, and mechanical systems [5]
Summary
Integral equations (IEs) are equations in which the unknown functions appear under one or more integral signs [1]. Delay integral equations (DIEs) are those IEs in which the solution of the unknown function is given in the previous time interval [2]. Zhao et al [8] used the Sinc collocation method for solving the DIEs. is technique reduces the DIEs of Volterra type to an explicit algebraic equation. E solution of these algebraic equations gives the solution of the Volterra DIEs. Yuzbasi and Ismailov [9] solved Volterra IEs with proportion delays by the method of differential transformation. Yuzbasi and Ismailov [9] solved Volterra IEs with proportion delays by the method of differential transformation In this technique, the solutions obtained are in the series form. For explicit derivation of the HWC technique, we consider ξ 1
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