Застосування методу двобічних наближень до розв’язання нелінійної крайової задач рівняння з бігармонічним оператором

Abstract

The aim is to apply the two-sided approximation method to solve the Dirichlet problem for a nonlinear equation with a biharmonic operator. The considered mathematical model appears during the process studying of deflection of a plate fixed at the boundary. In particular, this problem has found a wide applications in microelectromechanical systems. Thus, the current task is to develop numerical methods to solve it. In this study, we suggest to apply the two-sided approximation method based on the Green’s function using.