In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step method with the first step as Traub–Steffensen iteration and the next two taken as Traub–Steffensen-like iteration with four functional evaluations per iteration. We compare our proposed method with the recent derivative-free methods using some chemical engineering problems modelled as nonlinear equations with simple and multiple roots. Stability of the presented family of methods is demonstrated by using the graphical tool known as basins of attraction.
Among the various agro-industries, food processing industries are the second prime generator of wastes after domestic sewage. In the current epoch of the rapid budding world, the wastes are mounting, which robustly sway the health of ecosystems and eventually the human population. For that reason, each agro-industrial sector has critical stipulation toward the secure utilization of agro-materials all the way through recycling of wastes. A crude disposal and littering of these waste materials frequently signifies a problem that is additionally provoked by different legal restrictions. Inadequate management of these solid waste constituents could lead to drastic change in physico-chemical properties of soils. The waste product, which is discarded into the environment, is loaded with valuable compounds. They are new, innate, and monetary sources of colorants, protein, dietary fiber, flavoring, antimicrobials, and antioxidants, which can be utilized in the food industry as a basis of natural food additives.
Abstract.The availability of erratic rainfall and high evapotranspiration causes temporal and spatial variability of water thereby causing crop yield reduction and crop failure. The potential of water harvesting (WH) both groundwater as well as surface water to mitigate the spatial and temporal variability of precipitation. One technique for water harvesting (WH) is to collect excess runoff water both rain and snowmelt, store it for agricultural purposes during dry spells. The present work accentuated the expediency of remote sensing (RS) and geographic information system (GIS) applications in water harvesting studies. The resultant water harvesting potential map prepared was thus classified into three WH potential zones namely, high, medium and low covering an area of 32.82, 10320.10, and 7596.18 ha (<1%, 57.49%, and 42.32%) respectively. The groundwater map in the area was also classified as high potential areas covering 1421.69 ha (7.92%), medium potential areas covering 8762.69 ha (48.81%), and low potential areas covering 7764.72 ha (43.25%). The integrated remote sensing (RS), Geographical Information System (GIS), Soil and Water Assessment Tool (SWAT), and analytical hierarchy process (AHP) were found to be efficient methods to recover water and to select suitable water and groundwater harvesting sites in order to ensure better water accessibility to the people for domestic, irrigation and other activities in cold arid regions of northwestern Himalayas. Keywords: Analytical hierarchy process, Geographic Information System, Groundwater harvesting, Remote sensing, Spatial variability, Temporal variability, Water harvesting.
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