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Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation
Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
Department of Mathematics, Chukwuemeka Odimegwu Ojukwu University, Uli, Nigeria
Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
- 1 Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
- 2 Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
- 3 Department of Mathematics, Chukwuemeka Odimegwu Ojukwu University, Uli, Nigeria
- 4 Department of Mathematics, Michael Okpara University of Agriculture, Umuahia, Nigeria
World Journal of Mechanics·Volume 10 (2020)·Pages 210–219·Published 10 November 2020·DOI10.4236/wjm.2020.1011015
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Abstract
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.
KeywordsFrobenius MethodEigenvalue ApproachStabilityMathieu’s Equation
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