The primary focus of this article is on applying specific generalized Jacobi polynomials (GJPs) as basis functions to obtain the solution linear and non-linear even-order two-point BVPs. These GJPs are orthogonal that expressed Legendre polynomial combinations. BVPs treated using Petrov–Galerkin method. In addition, a formula for first-order derivative these in terms their original ones. This r...

This paper reveals the reliability and efficiency of two modified versions of variational iteration method (VIM) where He’s and Adomian’s polynomials have been inserted in the correction functional of the VIM. The comparison of the suggested algorithms has been made on sixth-order boundary value problems (BVPs) by converting them into systems of integral equations. The proposed modified version...

Third-order boundary-value problems for differential equation play a very important role in a variety of different areas of applied mathematics and physics. Recently, third-order boundary-value problems have been many scholars’ research object. For example, heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics can produce boundary-value problems wit...