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The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs

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Abstract

Many problems arising in different fields of sciences and engineering can be reduced, by applying some appropriate discretization, either to a system of integrodifferential algebraic equations or to a sequence of such systems. The aim of the present analysis is to implement a relatively recent computational method, reproducing kernel Hilbert space, for obtaining the solutions of integrodifferential algebraic systems of temporal two-point boundary value problems. Two extended inner product spaces W[0, 1] and H[0, 1] are constructed in which the boundary conditions of the systems are satisfied, while two smooth kernel functions R t (s) and r t (s) are used throughout the evolution of the algorithm in order to obtain the required grid points. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing kernel theory. In this approach, computational results of some numerical examples are presented to illustrate the viability, simplicity, and applicability of the algorithm developed.

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Acknowledgements

The authors express their thanks to unknown referees for the careful reading and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt, 19117, Jordan

    Omar Abu Arqub

  2. Department of Computer Science, P.A.B.G Faculty of Information Technology, Al-Balqa Applied University, Salt, 19117, Jordan

    Hasan Rashaideh

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  1. Omar Abu Arqub
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  2. Hasan Rashaideh
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Correspondence to Omar Abu Arqub.

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Abu Arqub, O., Rashaideh, H. The RKHS method for numerical treatment for integrodifferential algebraic systems of temporal two-point BVPs. Neural Comput & Applic 30, 2595–2606 (2018). https://doi.org/10.1007/s00521-017-2845-7

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  • DOI: https://doi.org/10.1007/s00521-017-2845-7

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