Application of Gegenbauer Polynomials and Mathieu Function to a Nonliner Dynamical System
by
N. K Choubey
Head of the Department Mathematics : Govt. Science College , Jabalpur, (M.P.) India

Abstract All Physical system in nature are generally nonlinear from the out set, hence they give rise to nonlinear differential equation . Such systems as pendulum executing large oscillations, the flow of electrical current in a circuit consisting of a capacitance in series with an iron cored inductance coil, the motion of mass restrained by a spring and undergoing friction are typical example of systems whose analysis leads to nonlinear differential equations. To avoid the difficulty of solving the nonlinear terms, we often neglect the nonlinear terms assuming them as they are small quantities but they must be taken into account to get the correct result. Denmann, Howard, Bhonsle and Garde have used Tchebycheff, Gegenbauer and Jacobi Polynomial approximation to study certain nonlinear system. This paper deals with the application of Gegenbuer Polynomials and Mathieu functions to nonlinear dynamical system. Finally numerical example is given to show that present Method and Fourier series approximation Method are very close.

Date received: September 5, 2003