Research on Numerical Methods of the Nonlinear Equations and its Applications

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We studied mainly on the numerical methods for polynomial equations, confluent hypergeometric functions, Mathieu's function and fractional differential equations. We studies some numerical methods for solving the polynomial equation and the characteristic values of Mathieu's function.We studied some nonhomogeneous fractional differential equations which have constant coefficients and tried to have the solution numerically. And we discuss an almost free damping vibration equation by means of N-fractional calculus.