Abstract
In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation in the space \(\oplus _{j=1}^2 W_2^3 \left[ {a,b}\right] \). An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.
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Author Omar Abu Arqub declares that he has no conflict of interest. Author Mohammed Al-Smadi declares that he has no conflict of interest. Author Shaher Momani declares that he has no conflict of interest. Author Tasawar Hayat declares that he has no conflict of interest.
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Arqub, O.A., Al-Smadi, M., Momani, S. et al. Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21, 7191–7206 (2017). https://doi.org/10.1007/s00500-016-2262-3
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DOI: https://doi.org/10.1007/s00500-016-2262-3