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- Mathematical Model of the Growth of Trees

- Numerical Model of the
- 27.08.2019

Mathematical Model of the Growth of Trees

Absract

At several stages of life, the expansion rate of any tree is usually not the same. This kind of presentation is always to: build a numerical model based on the regular style which has been seen and then fix the problem and optimize the established unit. Problem Idea

A newly grown tree increases slowly, yet gradually the tree develops tall and can grow in a faster speed. But when it develops to a certain height, the growth price will little by little become steady and then slowly and gradually go down. This kind of patter can be universal. Problem Analysis

If we imagine the growth price of a shrub is proportionate with its current height, it obviously would not meet the two ends, specially the latter part of the development process, as the tree will not grow faster and quicker boundlessly But if we assume that the growth rate of the forest is proportionate to the big difference between the optimum height plus the current height, it is clearly not in conformity with the middle area of the growth procedure. We produced a compromise assuming that the expansion rate is definitely proportional with both its current height and difference between maximum elevation and the current height. Presumptions

Assume that there is a maximum height of your tree can grow to, when this kind of height can be reached the tree will minimize growing larger. Assume that the expansion rate of a tree is merely related to its current elevation and the big difference between the optimum height as well as its current elevation, its not really influenced by simply other environmental factors. Mark Descriptors

Assume the maximum height from the tree is usually H (m) and at time t (year) the height is h(m). The proportional pourcentage of forest growth rate and the current height as well as the difference involving the maximum level and its current height is k. Version building and solving

In line with the analysis in the problem plus the assumptions manufactured above, we obtain the following equation:

Where the proportional continuous k > 0....

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