A load flow study referred to as a power flow study is a numerical analysis of the electricity that flows through any electrical power system. For instance, if a transmission line needs to be taken out of service for maintenance, load flow studies allow us to assess whether the remaining line can carry the load without exceeding its rated capacity. So, we need to understand about the voltage level and voltage phase angle on each bus under steady-state conditions to keep the bus voltage within a specific range. In this paper, our goal is to present a higher order efficient iterative method to carry out a power flow study to determine the voltages (magnitude and angle) for a specific load, generation and network conditions. We introduce a new seventh-order three-step iterative scheme for obtaining approximate solution of nonlinear systems of equations. We attain the seventh-order convergence by using four function evaluations which makes it worthy of interest. Moreover, we show its applicability to the electrical power system for calculating voltages and phase angles. By calculating the bus angle and voltage level, we conclude that the performance of the power system is assessed in a more efficient manner using the new scheme. In addition, dynamical planes of the methods applied on nonlinear systems of equations show global convergence.
Many real-life problems using mathematical modeling can be reduced to scalar and system of nonlinear equations. In this paper, we develop a family of three-step sixth-order method for solving nonlinear equations by employing weight functions in the second and third step of the scheme. Furthermore, we extend this family to the multidimensional case preserving the same order of convergence. Moreover, we have made numerical comparisons with the efficient methods of this domain to verify the suitability of our method.
The global positioning system (GPS) is a satellite navigation system that determines locations. Whenever the baseline satellites are serviced or deactivated, the Space Force often flies more than 24 GPS satellites to maintain coverage. The additional satellites are not regarded as a part of the core constellation but may improve the performance of the GPS. In this study of GPS models, we solved various problems. We examined each set of four satellites separately. Advancements in computer softwares have made computations much more precise. We can use iterative methods to solve GPS problems. Iterative schemes for solving nonlinear equations have always been of great importance because of their applicability to real-world problems. This paper involves the development of an efficient family of sixth-order Jarratt-type iterative schemes for analyzing nonlinear global positioning systems.
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