In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2...In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.展开更多
In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for stud...In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.展开更多
文摘In this paper we shall extend the paper [1] to a separate Taylor's Theorem with respect to a lot of centers, namely Newton's Theorem Of a lot of centers. From it we obtain the analogous results in the paper [2]. namely an interpolation formula of the difference of higher order. Finally we give their applications.
文摘In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.
