Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

Mondal, Sankar Prasad; Roy, Susmita; Das, Biswajit

doi:10.1155/2016/8150497

Cited by 9 publications

(2 citation statements)

References 39 publications

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“…The fourth-order and fifth-order Runge-Kutta-Fehlberg algorithm with a variable step size can be used to solve iteratively [26]. 1 Set the value of t 0 , t f , x 0 , h = 0.1, ε= 1e − 7, where h is the initial step size, and ε is the specified error control tolerance.…”

Section: Case Simulationmentioning

confidence: 99%

Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Dooling

et al. 2019

Sustainability

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Utilizing the urban water demand function and the Cobb-Douglas (C-D) production function, an economic control model for the multi-input-multi-output (MIMO) nonlinear system was designed and implemented to describe urban comprehensive water consumption, where the urban water demand function was expressed as the product of the number of water users and per capita comprehensive water consumption, and the urban water supply function was expressed as a C-D production function. The control variables included capital investment and labor input for the urban water supply. In contrast to the Solow model, Shell model and aggregate model with renewable labor resources, the proposed model eliminated value constraints on investment and labor input in the state equations and hence avoided the difficulty in applying these models to urban water supply institutions. Furthermore, the feedback linearization control design (FLCD) method was employed to accomplish stability of the system. In contrast to the optimal control method, the FLCD method possesses an explicit solution of the control law and does not require the solution of a two-point boundary value problem of an ordinary differential equation, making the method more convenient for application. Moreover, two different scenarios of urban water consumption, one for the growth period and the other for the decline period, were simulated to demonstrate the effectiveness of the proposed control scheme.

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Section: Case Simulationmentioning

confidence: 99%

Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Dooling

et al. 2019

Sustainability

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“…Since FDEs are applicable in many real life problems, researchers still need to improve and develop numerical methods in order to find better solutions for FDEs. More researchers in [18][19][20][21][22][23][24][25] have also proposed various methods to solve FDEs numerically. This study aims to improve the accuracy of the numerical solution of FDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical computation for solving fuzzy differential equations

Ishak

Chaini

2019

IJEECS

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Fuzzy differential equations (FDEs) play important roles in modeling dynamic systems in science, economics and engineering. The modeling roles are important because most problems in nature are indistinct and uncertain. Numerical methods are needed to solve FDEs since it is difficult to obtain exact solutions. Many approaches have been studied and explored by previous researchers to solve FDEs numerically. Most FDEs are solved by adapting numerical solutions of ordinary differential equations. In this study, we propose the extended Trapezoidal method to solve first order initial value problems of FDEs. The computed results are compared to that of Euler and Trapezoidal methods in terms of errors in order to test the accuracy and validity of the proposed method. The results shown that the extended Trapezoidal method is more accurate in terms of absolute error. Since the extended Trapezoidal method has shown to be an efficient method to solve FDEs, this brings an idea for future researchers to explore and improve the existing numerical methods for solving more general FDEs.

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The Transform Method to Solve Fuzzy Differential Equation via Differential Inclusions

Liu

Hong

2021

Advances in Fuzzy Integral and Differential Equations

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Numerical Solution of First-Order Linear Differential Equations in Fuzzy Environment by Runge-Kutta-Fehlberg Method and Its Application

Cited by 9 publications

References 39 publications

Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Numerical computation for solving fuzzy differential equations

The Transform Method to Solve Fuzzy Differential Equation via Differential Inclusions

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