Euler's Method to solve the Verhulst equation applied to fungal growth
DOI:
https://doi.org/10.35819/remat2022v8i1id5526Keywords:
Logistic Growth, Trunk Diseases in Grapevines, Euler Method, Modified Euler MethodAbstract
Mathematical modeling enables several contributions to development of society collaborating with scientific and technological advances. Through models, real phenomena are represented as is the case of fungal growth kinetics. This work uses the Verhulst equation, which characterizes the growth of a population up to the maximum capacity of the medium, solving it numerically by the one and two-stage Euler Method. The methodology is validated by comparing numerical and analytical solution available in the literature. The Verhulst model is applied considering some experimental parameters, which makes possible to determine the numerical solution of the equation in one and two stages. The simulated results presented a correspondence with the analytical solution with a smaller relative error between the solutions with the two-stage method. Thus, other methods can be adopted in future works aiming to minimize the error. Additionally, there is the possibility of employing the Euler method in more complex models since the exact solution is not always known.
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