Solution of the first order linear fuzzy differential equations by some reliable methods

Ghanbari, M.

doi:10.5899/2012/jfsva-00126

Cited by 13 publications

(15 citation statements)

References 40 publications

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“…In [16], the HPM was used to solve first order linear fuzzy initial value problems involving ordinary differential equations. The ADM was employed in [2,7,17] to solve first order linear and nonlinear fuzzy initial value problems. VIM is an approximate -analytical method that was first proposed by He [18][19][20][21][22] and has been applied to many physics and engineering problems [5,27,31,34].…”

Section: Introductionmentioning

confidence: 99%

“…VIM is an approximate -analytical method that was first proposed by He [18][19][20][21][22] and has been applied to many physics and engineering problems [5,27,31,34]. VIM was used in [17] to obtain the approximate solution for first order linear FIVP. Furthermore, it was found that VIM is more effective than ADM and the convergence of VIM is much faster than ADM.…”

Section: Introductionmentioning

confidence: 99%

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The Variational Iteration Method for Solving Fuzzy Duffing's Equation

Jameel¹

2014

Journal of Interpolation and Approximation in Scientific Comput

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In this paper, we use the Variational Iteration Method (VIM) to find the approximate analytical solution for an initial value problem involving the fuzzy Duffing ordinary differential equation. VIM allows for the solution of the differential equation to be calculated in the form of an infinite series in which the components can be easily computed. Numerical examples were solved to illustrate the capability of VIM in this regard. Definition 2.4. A mappingfor some interval is called a fuzzy function process [14] and we denote the r-level set by:The r-level sets of a fuzzy number are much more effective as representation forms of fuzzy set. Fuzzy sets can be defined by the families of their r-level sets based on the resolution, identity theorem [12,33].Definition 2.5. The fuzzy integral of fuzzy process [31], ̃( ) ∫ ̃( ) for and ,is defined by:of 14 4 Journal of Interpolation and Approximation in Scientific Computing

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Variational Iteration Method for Solving Fuzzy Duffing's Equation

Jameel¹

2014

Journal of Interpolation and Approximation in Scientific Comput

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“…We observe parametric form of the FVIE-2 is a system of Volterra integral equations of the second kind in crisp case. In Section 4, we state the basic concepts of the variational iteration method [7,13,14,15]. In Section 5, we apply variational iteration method on the linear system of Volterra integral equations of the second kind.…”

Section: Introductionmentioning

confidence: 99%

An application of a semi-analytical method on linear fuzzy Volterra integral equations

Allahviranloo¹,

Ghanbari²,

Nuraei³

2014

Journal of Fuzzy Set Valued Analysis

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Recently, fuzzy integral equations have attracted some interest. In this paper, we focus on linear fuzzy Volterra integral equation of the second kind (FVIE-2) and propose a new method for numerical solving it. In fact, using parametric form of fuzzy numbers we convert a linear fuzzy Volterra integral equation of the second kind to a linear system of Volterra integral equations of the second kind in crisp case. We use variational iteration method (VIM) and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Volterra integral equation of the second kind. Finally, using the proposed method, we give some illustrative examples.

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“…In [12], the HPM was used to solve first order linear fuzzy initial value problems involving ordinary differential equations. The ADM was employed in [13,14] to solve first order linear and nonlinear FDEs. Furthermore, in [14] it was found that VIM is more effective than ADM and the convergence of VIM is much faster than ADM. Also, in [15] VIM was used to find the semi-analytical solution for fuzzy differential equations including nonlinear first order problem.…”

Section: Introductionmentioning

confidence: 99%

“…The ADM was employed in [13,14] to solve first order linear and nonlinear FDEs. Furthermore, in [14] it was found that VIM is more effective than ADM and the convergence of VIM is much faster than ADM. Also, in [15] VIM was used to find the semi-analytical solution for fuzzy differential equations including nonlinear first order problem. Abbasbandy et al in [16] used VIM to find the approximate solution for high order linear FIVP by converted it into first order system of fuzzy differential equations.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Solution of Heat Equation in Fuzzy Environment

Jameel¹

2014

IJAPM

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Abstract:In this paper, we develop and analyze the use of the Variational Iteration Method (VIM) to find the semi-analytical solution for an initial value problem involving the fuzzy heat parabolic equation. VIM allows for the solution of the partial differential equation to be calculated in the form of an infinite series in which the components can be easily computed. The VIM will be studied for fuzzy initial value problems involving partial parabolic differential equations. Also VIM will be constructed and formulated to obtain a semi-analytical solution of fuzzy heat equation by using the properties of fuzzy set theory. Numerical example involving fuzzy heat equation was solved to illustrate the capability of VIM in this regard. The numerical results that obtained by VIM were compared with the exact solution in the form of Table I-Table II and Fig. 1-Fig. 2.

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Solution of the first order linear fuzzy differential equations by some reliable methods

Cited by 13 publications

References 40 publications

The Variational Iteration Method for Solving Fuzzy Duffing's Equation

The Variational Iteration Method for Solving Fuzzy Duffing's Equation

An application of a semi-analytical method on linear fuzzy Volterra integral equations

Semi-Analytical Solution of Heat Equation in Fuzzy Environment

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