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Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm

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Abstract

The aim of the present analysis is to implement a relatively recent computational algorithm, reproducing kernel Hilbert space, for obtaining the solutions of systems of first-order, two-point boundary value problems for ordinary differential equations. The reproducing kernel Hilbert space is constructed in which the initial–final conditions of the systems are satisfied. Whilst, three smooth kernel functions 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. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods.

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Acknowledgements

The author would like to express his gratitude to the unknown referees for carefully reading the paper and their helpful comments.

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

    Omar Abu Arqub

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  1. Omar Abu Arqub
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Correspondence to Omar Abu Arqub.

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Abu Arqub, O. Numerical solutions of systems of first-order, two-point BVPs based on the reproducing kernel algorithm. Calcolo 55, 31 (2018). https://doi.org/10.1007/s10092-018-0274-3

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