Numerical Solutions of Sixth Order Eigenvalue Problems Using Galerkin Weighted Residual Method

In this research article, we present Galerkin weighted residual (WRM) technique to find the numerically approximated eigenvalues of the sixth order linear Sturm–Liouville problems (SLP) and Bénard layer problems. In the current method, Bernstein polynomials are being employed as the basis functions and precise matrix formulation is derived for solving eigenvalue problems. Numerical examples with homogeneous boundary conditions are considered to verify the efficiency and implementation of the proposed method. The numerical results offered in this paper are also compared with those investigated by other numerical/analytical methods and the computed eigenvalues are in good agreement.