Functions and Analysis


An Efficient Computational Method for Handling Singular Second-Order, Three Points Volterra Integrodifferenital Equations

Authors: Morad Ahmad, Shaher Momani, Omar Abu Arqub, Mohammed Al-Smadi, Ahmed Alsaedi

In this paper, a powerful computational algorithm is developed for the solution of classes of singular second-order, three-point Volterra integrodifferential equations in favorable reproducing kernel Hilbert spaces. The solutions is represented in the form of series in the Hilbert space W₂³[0,1] with easily computable components. In finding the computational solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. Error estimates are proven that it converge to zero in the sense of the space norm. Several computational simulation experiments are given to show the good performance of the proposed procedure. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to multipoint singular boundary value problems restricted by Volterra operator.

Comments: 13 Pages.

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Submission history

[v1] 2017-05-02 15:33:07

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