Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems

Sharmila, R.

doi:10.9790/5728-1302024351

Cited by 2 publications

(1 citation statement)

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“…The proposed work is based on RK-method using geometric mean for incremental function and first such work based on mean is introduced by Sanugi [9] who developed explicit RK-method based on geometric mean. The nth order fuzzy initial value problem is solved by fourth order RK method using centroidal mean [10] and contra harmonic mean based RK method of fourth order is used to approximate initial value problem (IVP) [11]. The method developed in the proposed work is an extended form of the RK-method of third order based on geometric mean [12], [13] and the various techniques developed so far for solving different types of differential equations using RK-method is critically reviewed by Chauhan and Srivastava [14].…”

Section: Introductionmentioning

confidence: 99%

Tetra geoemtric mean Runge-Kutta analysis of bioeconomic fisheries model

Chauhan,

Srivastava

2023

BUT_Series_III

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The optimal management and utilization of natural resources is eventually important, due to increase in the consumption of natural resources and in view of this, the main aim of fisheries is to maintain the marine organisms at levels that produces maximum sustainable yield (MSY). In this study, the one step numerical approximations schemes are developed to find the solution of such bioeconomic fisheries models whose analytical solution is not possible. In the proposed work, the explicit Runge-Kutta scheme based on fourth order tetra geometric mean is established and this method solve fishery management models of Schaefer and Gordon-Schaefer. The models analyze bioeconomic growth rate, carrying capacity, total and marginal costs and revenues. In solving, the models through proposed tetra geometric mean Runge-Kutta method, it is obtained that the method is easy to implement. The results obtained are much better as compared to other methods when compared in terms of errors and central processing unit (CPU) time.

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