Oscillations of coronal loops using Rayleigh-Ritz technique

In this paper, we apply the Rayleigh-Ritz Variational Scheme for studying the transverse oscillations of a magnetic flux tube. The flux tube is considered in low-$\beta$ solar coronal condition. The perturbations decomposed into irrotational and solenoidal components and MHD equations are reduced as a matrix eigenvalue problem. In the case of longitudinally stratified thin flux tube, the fundamental and higher order kink frequencies are computed. The results are in good agreements with previous studies.