A Comparison of Newly Developed Broyden – Like Methods for Solving System of Nonlinear Equations
Azure Isaac,
Twum Boakye Stephen,
Baba Seidu
Issue:
Volume 6, Issue 3, September 2021
Pages:
77-94
Received:
10 July 2021
Accepted:
20 July 2021
Published:
24 July 2021
Abstract: The search for a more efficient and robust numerical method for solving problems have become an interesting area for many researchers as most problems resulting into nonlinear system of equations would require a very good numerical method for its computation. The introduction of the Broyden method has served as the foundation to developing several others, which are referred to as Broyden – like methods by some authors. These methods, in most cases, have proven to be superior to the original classical Broyden method in terms of the number of iterations needed and the CPU time required to reach a solution. This research sought to develop new Broyden – like methods using weighted combinations of quadrature rules (i.e., Simpson -1/3 and Simpson -3/8 rules against Midpoint, Trapezoidal, and Simpson quadrature rules). The weighted combination of the quadrature rules in the development of the new methods led to the discovery of several new methods. Some of which have proven to be more efficient and robust when compared with some existing methods. A comparison of these newly developed methods with the classical Broyden method together with some existing improved Broyden method revealed that, one of the newly developed methods namely, Midpoint–Simpson-3/8 (MS–3/8) method, outperformed all the others, with the MS–3/8 method giving the best of numerical results in all the benchmark problems considered in the study.
Abstract: The search for a more efficient and robust numerical method for solving problems have become an interesting area for many researchers as most problems resulting into nonlinear system of equations would require a very good numerical method for its computation. The introduction of the Broyden method has served as the foundation to developing several ...
Show More
Logistics Network Design for Vegetable Waste Reduction and Recycling System Based on Multi-dimensional Perspective
Juan Yang,
Yongliang Liu,
Haorui Liu
Issue:
Volume 6, Issue 3, September 2021
Pages:
95-110
Received:
27 June 2021
Accepted:
22 July 2021
Published:
29 July 2021
Abstract: Aiming at the problem of insufficient recycling and recycling of vegetable wastes, under the conditions of three different on-site processing capabilities, the logistics network design scheme of vegetable waste reduction and resource utilization system was discussed. the present study discussed a quantitative model of the VW-RRS that meets comprehensive benefits based on the theory of circular economy, combined with reverse logistics theory and life cycle theory, and further designed a logistics network of VW-RRS from multi-dimensional perspectives. For the systematic VW treatment, the efficiency of the circular economy system has an obvious promotion effect. Based on the functions and interrelationships of the various participants in the system and the goal of achieving sustainable development in the three dimensions of economy, environment and society, a logistics network model of a reduced resource system has been established. Take Shouguang City as an example to optimize and reconstruct the logistics network of vegetable waste reduction in this region. The research shows that: after the vegetable waste is reduced, the total cost of the system is reduced; when the vegetable waste resource utilization capacity remains unchanged, the ratio of vegetable waste recycling is increased, and the economic and environmental benefits of the system are improved accordingly; The resource utilization capacity, the system's economic and environmental benefits have also improved accordingly.
Abstract: Aiming at the problem of insufficient recycling and recycling of vegetable wastes, under the conditions of three different on-site processing capabilities, the logistics network design scheme of vegetable waste reduction and resource utilization system was discussed. the present study discussed a quantitative model of the VW-RRS that meets comprehe...
Show More
