The Taylor series method and trapezoidal rule on time scales

2020 ◽  
Vol 378 ◽  
pp. 125200
Author(s):  
Svetlin G. Georgiev ◽  
İnci M. Erhan
Author(s):  
Svetlin Georgiev ◽  
Inci Erhan

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order $p$ on time scales. The error and convergence analysis of the method is also obtained. The 2 step Adams-Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.


Author(s):  
Jirí Kunovský ◽  
Martina Drozdová ◽  
Jirí Petrek ◽  
Pavla Sehnalová ◽  
František Zboril

2014 ◽  
Vol 960-961 ◽  
pp. 1039-1042
Author(s):  
Gui Hua Lin ◽  
Yu Ying Wang ◽  
Tao Wang

Take full advantage of the PMU's accurate mass measurement data is the effective method to improve the calculation accuracy of power system state estimation. This essay puts forward the state estimation method of power system based on the Taylor series method. It analysis of power system operating conditions based on the real-time measurement of Wide area measurement system, divides the state time, establishes the equation of state of the measurement data by curve fitting method in the period of state time, creates a new state estimation calculation method by Taylor series method, constructs a new voltage characteristic curve calculation method, determines the system state and achieve the continuity of power systems steady-state analysis. The method put forward in this essay has been verified through IEEE-30 Node System, and the efficiency of it has been fully proved by the example results.


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