Numerical solution of system of two Nonlinear Volterra Integral equations

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.

Parallel Algorithm for Transient Stability Online Simulation

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.