Asiyeh Ebrahimzadeh - Assistent Professor, Department of Mathematics Education, Farhangian University, Tehran, Iran
Samaneh Panjeh Ali Beik - National Center of Medical Education Assessment, Tehran, Iran

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.

Hinged Beam, Spectral method, Nonlinear fourth order boundary value problem, Shifted Legendre polynomials, Operational matrix of derivative