On the fuzzy difference equations of finance

Chrysafis, Konstantinos A.; Papadopoulos, Basil K.; Papaschinopoulos, G.

doi:10.1016/j.fss.2008.06.007

Cited by 47 publications

(30 citation statements)

References 12 publications

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“…Problem 1 [9] y ′ (t) = y(t), : Fourth order Runge-Kutta method 2P1D1 (4) : Fourth order two-point one block diagonally implicit multistep method…”

Section: Numerical Resultsmentioning

confidence: 99%

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Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

Ramli¹,

Majid²

2016

Int. J. of Pure and Appl. Math.

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Abstract:A fourth order diagonally implicit multistep block method is introduced to approximate the solution of fuzzy differential equations (FDEs). The problem is interpreted by using Seikkala's derivative. This method approximates two points simultaneously in a block along the interval. The Lagrange interpolating polynomial is applied in the formation of the formulas. The stability and convergence of this method at each computation points are given. Numerical solutions of this method are compared with the Runge-Kutta method of order four (RK(4)). The numerical results are given to highlight the performance of the proposed method when solving FDEs.

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“…Problem 1 [9] y ′ (t) = y(t), : Fourth order Runge-Kutta method 2P1D1 (4) : Fourth order two-point one block diagonally implicit multistep method…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The first-order linear FDEs occurred in many real-world applications such as engineering [1], medicine (see [2], [3]), finance [4] and population models [5]. The problems are permeating with uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

Ramli¹,

Majid²

2016

Int. J. of Pure and Appl. Math.

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“…If gcd(r, m) = s > 1, then we consider the max-type equation y n = max{ 1 z n−sm 1 , α n z n−sr 1 }, z n = max{ 1 y n−sm 1 , β n y n−sr 1 }, n = 0, 1, 2, . .…”

Section: Corollary 33 There Exists a Sequencementioning

confidence: 99%

“…, By an analogous way as in the above, we know that {(y i n , z i n )} n 0 is a positive solution of (3.4) for every 0 i s − 1. Then {(y i n , z i n )} n 0 is eventually periodic with period 2m 1 . Therefore {(y n , z n )} n 0 is eventually periodic with period 2m.…”

Section: Corollary 33 There Exists a Sequencementioning

confidence: 99%

Dynamics of the fuzzy difference equation z n = max { 1 z n − m , α n z n − r }

Sun¹,

Xi²,

Su³

et al. 2018

J. Nonlinear Sci. Appl.

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“…It not only enriched the theory of mathematics, but also solved the practical problem, such as the fields of the number of population structure analysis, economic, genetic, biology etc. (see, eg., [1][2][3][4][5] and the references therein). In recent years, research on discrete systems has become a hot problem.…”

Section: Introductionmentioning

confidence: 99%

Boundedness and Asymptotic Behaviour of the Solutions for a Third- Order Fuzzy Difference Equation

Jing¹,

Li²,

Wang³

2019

IOTCC

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Our aim in this paper is to investigate the dynamics of a third-order fuzzy difference equation. By using new iteration method for the more general nonlinear difference equations and inequality skills as well as a comparison theorem for the fuzzy difference equation, some sufficient conditions which guarantee the existence, unstability and global asymptotic stability of the equilibriums for the nonlinear fuzzy system are obtained. Moreover, some numerical solutions of the equation describing the system are given to verify our theoretical results.

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On the fuzzy difference equations of finance

Cited by 47 publications

References 12 publications

Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

Dynamics of the fuzzy difference equation z n = max { 1 z n − m , α n z n − r }

Boundedness and Asymptotic Behaviour of the Solutions for a Third- Order Fuzzy Difference Equation

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