A numerical method based on the reproducing kernel Hilbert space method for the solution of fifth-order boundary-value problems

TL;DR

This paper introduces a fast, accurate numerical scheme using the reproducing kernel Hilbert space method for solving fifth-order boundary-value problems, demonstrating superior efficiency and accuracy over existing methods.

Contribution

The paper develops a novel numerical approach based on RKHSM specifically tailored for fifth-order boundary-value problems, with analytical solutions expressed as convergent series.

Findings

Results are validated against exact solutions.

The method outperforms spline, decomposition, and variational iteration methods.

Numerical examples confirm high accuracy and efficiency.

Abstract

In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the equations have been obtained in terms of convergent series with easily computable components. We compare our results with spline methods, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation methods. The comparison of the results with exact ones is made to confirm the validity and efficiency.