  In this article, the reproducing kernel Hilbert space [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 result 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.
