Title :
A new numerical method of nonlinear equations by four order Runge-Kutta method
Author :
Lin, Ruitao ; Wang, Chan ; Liu, Fang ; Xu, Yueliang
Author_Institution :
Coll. of Mathematic, South-West Jiaotong Univ., Chengdu, China
Abstract :
In this paper, we use homotopy method to transfer nonlinear equations to a differential equations, then we apply four-order Runge-Kutta method to solve the differential equations for getting a more stable and easily convergent solution. What is more important, we demonstrate a complete proof of the whole process, which provide a scientific foundation for the method as a whole. In the end, we give a specific example that is solved by the approach we have proved, which shows the efficiency and stability of the method. With the new methods, some certain nonlinear equations can be simply and precisely caculated, which can contribute to production planning and control or operation problems significantly.
Keywords :
Runge-Kutta methods; nonlinear differential equations; numerical stability; production control; production planning; convergence; differential equations; four order Runge-Kutta method; homotopy method; nonlinear equation; numerical method; operation problems; production control; production planning; stability; Artificial neural networks; Differential equations; Iterative methods; Mathematical model; Nonlinear equations; Presses; convergence stability; four-order Runge-Kutta method; homotopy method;
Conference_Titel :
Industrial Engineering and Engineering Management (IEEM), 2010 IEEE International Conference on
Conference_Location :
Macao
Print_ISBN :
978-1-4244-8501-7
Electronic_ISBN :
2157-3611
DOI :
10.1109/IEEM.2010.5674394