Multistage Bernstein collocation method for solving strongly nonlinear damped systems

Abstract

In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated include step function external excitation and periodical function external excitation. We found that the MBCM gives more accurate approximate solutions than the standard collocation method. Since MBCM splits the domain of the problem [a,b] into n parts, one can overcome oscillations arising from the standard collocation method by increasing n. The results obtained from MBCM compare favorably with that of the fourth-order Runge-Kutta method (RK4).