numerical solution of differential equations of elastic curves in 3-dimensional anti-de sitter space

In this paper, we aim to extend the darboux frame field into 3-dimensional anti-de sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the euler-lagrange equations and derive differential equations for non-null elastic curves in ads$_{3}$ (i.e. 3-dimensional anti-de sitter space). in this study, we investigate the elastic curves in ads$_{3}$ and obtain equations through which elastic curves are found out. therefore, we solve these equations numerically and finally plot and design some elastic curves.