Soft Computing

, Volume 21, Issue 23, pp 7191–7206 | Cite as

Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

  • Omar Abu Arqub
  • Mohammed Al-Smadi
  • Shaher Momani
  • Tasawar Hayat
Methodologies and Application

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.

Keywords

Fuzzy boundary value problems Reproducing kernel theory Strongly generalized differentiability Gram–Schmidt process 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Omar Abu Arqub
    • 1
  • Mohammed Al-Smadi
    • 2
  • Shaher Momani
    • 3
  • Tasawar Hayat
    • 4
  1. 1.Department of Mathematics, Faculty of ScienceAl Balqa Applied UniversitySaltJordan
  2. 2.Department of Applied Science, Ajloun CollegeAl Balqa Applied UniversityAjlounJordan
  3. 3.Department of Mathematics, Faculty of ScienceUniversity of JordanAmmanJordan
  4. 4.Department of Mathematics, Faculty of ScienceQuaid-I-Azam UniversityIslamabadPakistan

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