Variational iteration algorithm for numerical solutions of sixth and seventh order boundary value problems using shifted Vieta-Lucas polynomials

Abstract

This study employs Shifted Vieta-Lucas Polynomials using the variational iteration approach to numerically resolve sixth and seventh order Boundary Value Problems (BVPs), The proposed method in the study is used, with the trial functions for the approximation being the shifted Vieta Lucas polynomials generated for the given boundary value problem. The study provides an efficient and accurate solutions to higher-order BVPs using a combination of Shifted Vieta-Lucas Polynomials and the variational iteration approach and finds applications in mathematics and other fields of sciences and engineering.

Keywords

• Variational iteration technique
• Boundary value problems
• Shifted vieta-lucas polynomials
• Approximate solutions