Spectral Solutions of Even-Order BVPs Based on New Operational Matrix of Derivatives of Generalized Jacobi Polynomials

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 relation key constructing an operational matrix can be used treat fact, numerical approach proposed derivatives convert differential equations into effectively solvable systems equations. convergence expansion investigated. To show precision viability our suggested algorithms, some examples given.