implicit trapezoidal rule
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2014 ◽  
Vol 12 (10) ◽  
pp. 3967-3975
Author(s):  
Dalal Adnan Maturi

In this paper, using the implicit trapezoidal rule in conjunction with Newton's method to solve nonlinear system.We have used a Maple 17 program to solve the System of two nonlinear Volterra integral equations. Finally, several illustrative examples are presented to show the effectiveness and accuracy of this method.


2012 ◽  
Vol 433-440 ◽  
pp. 4446-4451
Author(s):  
Tian Liang Xue ◽  
Fang Zong Wang ◽  
Jing Ye

Parallel computation is an effective approach to real-time simulation and transient stability online assessment of large-scale power systems. In this paper, the s-stage 2s-order symplectic Runge-Kutta-Nyström method is adopted for transient stability simulation of power system using classic model. Using Butcher transformation, a new parallel algorithm has been derived. The proposed algorithm has the convergence characteristic of a Newton type method and is of fully parallel-in-time. Through numerical simulation where the IEEE 145-bus power system is used, the proposed algorithm has been tested and compared with the conventional parallel-in-time Newton approach using implicit trapezoidal rule.


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