Topic
Direct method
About: Direct method is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 32565 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors used the techniques of cluster analysis to split the treatments into reasonably homogeneous groups and developed a likelihood ratio test for judging the significance of differences among the resulting groups.
Abstract: It is sometimes useful in an analysis of variance to split the treatments into reasonably homogeneous groups. Multiple comparison procedures are often used for this purpose, but a more direct method is to use the techniques of cluster analysis. This approach is illustrated for several sets of data, and a likelihood ratio test is developed for judging the significance of differences among the resulting groups.
3,050 citations
2,408 citations
TL;DR: In this paper, a direct approach for unbalanced three-phase distribution load flow solutions is proposed, where two developed matrices, the bus-injection to branch-current matrix and the branchcurrent to busvoltage matrix, and a simple matrix multiplication are used to obtain load flow solution.
Abstract: A direct approach for unbalanced three-phase distribution load flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two developed matrices-the bus-injection to branch-current matrix and the branch-current to bus-voltage matrix-and a simple matrix multiplication are used to obtain load flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or Y admittance matrix required in the traditional load flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.
1,074 citations
TL;DR: Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations and results for the fifth-order method are disappointing, but both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods.
849 citations
TL;DR: A special direct collocation method that can be used in combination with multiple shooting and a hybrid approach to improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods are presented.
Abstract: This paper gives a brief list of commonly used direct and indirect efficient methods for the numerical solution of optimal control problems. To improve the low accuracy of the direct methods and to increase the convergence areas of the indirect methods we suggest a hybrid approach. For this a special direct collocation method is presented. In a hybrid approach this direct method can be used in combination with multiple shooting. Numerical examples illustrate the direct method and the hybrid approach.
812 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 31 |
| 2020 | 46 |
| 2019 | 38 |
| 2018 | 27 |
| 2017 | 41 |