Author(s)

Everestus Obinwanne Eze^1*, Uchenna Emmanuel Obasi¹, Rosary Ngozi Ujumadu², Grace Ihuoma Kalu¹

¹Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria.
²Department of Mathematics, Chukwuemeka Odimegwu Ojukwu University, Uli, Nigeria.

This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and Eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.

Frobenius Method, Eigenvalue Approach, Stability, Mathieu’s Equation

Eze, E. , Obasi, U. , Ujumadu, R. and Kalu, G. (2020) Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation. World Journal of Mechanics, 10, 210-219. doi: 10.4236/wjm.2020.1011015.