Application of spectral methods to solve nonlinear buckling analysis of an elastic beam

This study is concerned with exploiting the spectral method to solve the fourth-order boundary value problem (bvp). such equations frequently arise in the study and modeling of large amplitude transverse buckling in an elastic beam. to this end, the properties of shifted legendre polynomial together with its operational matrix of the derivative and the spectral method is utilized to reduce bvp to a system of algebraic equations. numerical results turn out the efficiency and accuracy of the propounded technique.