Runge method
2.The Algorithm Design of Autoselect Step Runge-Kutta Method of Four Order
3.The numerical values of the one order differential equations are obtained by Runge-Kutta method with variable step.
6.In view of fourth-oder Runge-Kutta Method,a way of obtaining an optimum stepsize is Presented, which can assure the accuracy and stability of convergence.
7.The characteristics of x2k+1(k=0,1,2,…) oscillators is simulated and visualized using Runge-Kutter method with Matlab,Matlab code and a graphical user interface(GUI) are presented.
8.Numerical calculations on Josephson junctions under microwave radiation are made by means of Runge-Kutta method in the RSJ model. The DC I-V curves of Josephson junctions reproduce experimental results very well.
9.We apply Lie group method and Cayley transformation to construct high order explicit square conserving scheme for the modulus conserving differential equations, such as the Euler equation, the Landau-Lifshitz equation and compare the numerical results with the classical Runge-Kutta method in modulus conserving and accuracy. Numerical experiments results show that the new explicit square conserving scheme can preserve the modulus conserving property and the same accuracy as the corresponding classical Runge-Kutta methods.
10.All of the numerical analysis is based on the Runge-Kutta method of 4,5 step algorithm, the algorithm can guarantee a certain accuracy, but without affecting the temporal complication and spatial complication in computations.
