Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations

Shang, Dequan; Xiao, Guo

doi:10.1155/2013/312328

Cited by 8 publications

(20 citation statements)

References 31 publications

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“…For instance, some environmental factors or economical activities that affect the survival of the species may precipitously cause the growth to be either in increasing or decreasing motion. Furthermore, Tables 2-5 ratify stability and originality of the numerical solutions obtained by utilizing the well-known methods, namely FFRK, GL [15], and ABM [38]. (30,35,40).…”

Section: Implementation Of Fuzzy Fractional Laplace Transformmentioning

confidence: 99%

“…Some equilibrium points with fractional index are also obtained to further study the historical state of constant solutions. Additionally, we explore a comparative analysis between FFRK, Grunwald-Letnikov's definition (GL) [15], and Adams-Bashforth method (ABM) [38]. These techniques are widely known approximators to fractional and integer order differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

et al. 2019

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The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with imprecise biological parameters and fractional order generalized Hukuhara (fgH) differentiability. In this vain, different possible systems of the model are constructed, according to the increasing and decreasing behavior of population growth. Feasibility and stability analyses of equilibrium points of the stated models are also discussed by means of variational matrix with Routh–Hurwitz conditions. In addition, the numerical elaborations are carried out by taking parametric expansion of fuzzy fractional Laplace transform (FFLT). This significantly helps the researchers in using a novel approach to analyze the constant solutions of the dynamical systems in the presence of fractional index. This would allow the avoidance of any intricacy that occurs while solving fractional order derivatives. Furthermore, this attempt also provides numerical and pictorial results, obtained through some well-known methods, namely fifth-forth Runge–Kutta method (FFRK), Grunwald–Letnikov’s definition (GL) and Adams–Bashforth method (ABM) that are deemed appropriate to scrutinize the dynamics of the system of equations.

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Section: Implementation Of Fuzzy Fractional Laplace Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

et al. 2019

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“…This inexactitude extends to the requirement of fuzzy differential equations (FDEs) to surmount the problem. This aspect of fuzzy differential equations takes place in numerous studies like scientific discipline, economic science, psychological science, defense mechanism, human ecology and applied sciences [17], [23], [36] and [39].…”

Section: Introductionmentioning

confidence: 99%

The Extended Block Predictor-Block Corrector Method for Computing Fuzzy Differential Equations

Oghonyon

Egharevba

Imaga

2022

Wseas Transactions on Mathematics

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Over the years, scholars have developed predictor-corrector method to provide estimates for ordinary differential equations (ODEs). Predictor-corrector methods have been reduced to predicting-correcting method with no concern for finding the convergence-criteria for each loop with no suitable vary step size in order to maximize error. This study aim to consider computing fuzzy differential equations employing the extended block predictor-block corrector method (EBP-BCM). The method of interpolation and collocation combined with multinomial power series as the basis function approximation will used. The principal local truncation errors of the block predictor-block corrector method will be utilized to bring forth the convergence criteria to ensure speedy convergence of each iteration thereby maximizing error(s). Thus, these findings will reveal the ability of this technique to speed up the rate of convergence as a result of variegating the step size and to ensure error control. Some examples will solve to showcase the efficiency and accuracy of this technique.

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“…In recent times, many ways and means are being established to analyze and simulate fuzzy differential equations. For instance, Euler type methods [4], shooting method [5], fuzzy Picard method [6], fuzzy Laplace transform [7], fuzzy Sumudu transform [8], Runge-Kutta method [9]- [10], fuzzy variational iteration method [11], Adams predictor corrector [12], Taylor method [13], modified Homotopy perturbation method [14], to name a few. Along with these techniques, various papers are found where the latest methods, like different artificial neural networks [15]- [16], are also carried out for the evaluation of FDEs.…”

Section: Introductionmentioning

confidence: 99%

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

Ara

Razzaq

Khan

2018

Annals of West University of Timisoara - Mathematics and Computer Science

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Bearing in mind the considerable importance of fuzzy differential equations (FDEs) in different fields of science and engineering, in this paper, nonlinear nth order FDEs are approximated, heuristically. The analysis is carried out on using Chebyshev neural network (ChNN), which is a type of single layer functional link artificial neural network (FLANN). Besides, explication of generalized Hukuhara differentiability (gH-differentiability) is also added for the nth order differentiability of fuzzy-valued functions. Moreover, general formulation of the structure of ChNN for the governing problem is described and assessed on some examples of nonlinear FDEs. In addition, comparison analysis of the proposed method with Runge-Kutta method is added and also portrayed the error bars that clarify the feasibility of attained solutions and validity of the method.

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Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations

Cited by 8 publications

References 31 publications

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

The Extended Block Predictor-Block Corrector Method for Computing Fuzzy Differential Equations

A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations

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