The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,th...The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.展开更多
An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed,using the multi-step differential transform method based o...An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed,using the multi-step differential transform method based on the classical differential transformation method.Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the precision and effectiveness of the proposed method.Results are given in explicit and graphical forms.展开更多
文摘The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
文摘An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed,using the multi-step differential transform method based on the classical differential transformation method.Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the precision and effectiveness of the proposed method.Results are given in explicit and graphical forms.
