Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

The numerical approximation of eigenvalues of higher even order boundary value problems has sparked a lot of interest in recent years. However, it is always difficult to deal with higher-order BVPs because of the presence of boundary conditions. The objective of this work is to investigate a few higher order eigenvalue (Rayleigh numbers) problems utilizing the method of Galerkin weighted residual (MWR) and the effect of solution due to direct implementation of polynomial bases. The proposed method develops a precise matrix formulation for the eighth order eigenvalue and linear electro-hydrodynamic (EHD) stability problems. • The article explores the same for tenth and twelfth order eigenvalue problems. • This method involves computing numerical eigenvalues using Bernstein polynomials as the basis functions. • The novel weighted residual Galerkin technique's performance is numerically validated by comparing it to other numerical/analytical approaches in the literature.