Research Article Open Access

Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

Asad Freihat1, Radwan Abu-Gdairi2, Hammad Khalil3, Eman Abuteen4, Mohammed Al-Smadi1 and Rahmat Ali Khan3
  • 1 Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan
  • 2 Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
  • 3 Department of Mathematics, University of Malakand, Chakadara Dir(L), Khyber Pakhtunkhwa, Pakistan
  • 4 Department of Applied Science, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11942, Jordan


In this article, the reproducing kernel Hilbert space W24  [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The analytic solution is formulated in a finite series form whilst the truncated series solution is given to converge uniformly to analytic solution. The reproducing kernel procedure is based upon generating orthonormal basis system over a compact dense interval in sobolev space to construct a suitable analytical-numerical solution. Furthermore, experiments results of some numerical examples are presented to illustrate the good performance of the presented algorithm. The results indicate that the reproducing kernel procedure is powerful tool for solving other problems of ordinary and partial differential equations arising in physics, computer and engineering fields.

American Journal of Applied Sciences
Volume 13 No. 5, 2016, 501-510


Submitted On: 9 December 2015 Published On: 11 May 2016

How to Cite: Freihat, A., Abu-Gdairi, R., Khalil, H., Abuteen, E., Al-Smadi, M. & Khan, R. A. (2016). Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems. American Journal of Applied Sciences, 13(5), 501-510.

  • 8 Citations



  • Boundary Value Problem
  • Error Estimation and Error Bound
  • Reproducing Kernel Theory