Abstract
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.
Highlights
Periodic Boundary Value Problem (PBVP) is an active research of modern mathematics that can be found naturally in different branches of applied sciences, physics and engineering (Gregu, 1987; Minh, 1998; Ashyralyev et al, 2009)
[0, 1], y(t) satisfy periodic conditions of Equation 8, which means that y(t) is analytic solution of Equation 7 and 8 such that y(t) =
We introduce the fitting reproducing kernel approach to enlarge its application range for treating a class of third-order periodic BVPs in a favorable reproducing kernel Hilbert space
Summary
Periodic Boundary Value Problem (PBVP) is an active research of modern mathematics that can be found naturally in different branches of applied sciences, physics and engineering (Gregu, 1987; Minh, 1998; Ashyralyev et al, 2009). The purpose of this analysis is to develop analytical-numerical method for handling third-order, two-point PBVP with given periodic conditions by an application of the reproducing kernel theory. The n-term numerical solution is obtained to converge uniformly to analytic solution.
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