Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Arqub, Omar Abu

doi:10.1007/s00521-015-2110-x

Cited by 343 publications

(73 citation statements)

References 52 publications

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“…In recent years, the reproducing kernel Hilbert space method has been used for obtaining approximate solutions in a wide class of ordinary differential, partial differential and integral equations. Please refer to [4,6,7,8,22,24,28,29]. Among plethora of studies addressing the reproduction of kernel Hilbert space method for solving various problems and even among a bunch of extensive works related to reproducing kernel Hilbert spaces for solving ordinary equation, we just mention a number of more interesting problems.…”

Section: Introductionmentioning

confidence: 99%

Generalized Jacobi Reproducing Kernel Method in Hilbert Spaces for Solving the Black-Scholes Option Pricing Problem Arising in Financial Modelling

Foroutan

Ebadian

Fazli

2018

Mathematical Modelling and Analysis

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Based on the reproducing kernel Hilbert space method, a new approach is proposed to approximate the solution of the Black-Scholes equation with Dirichlet boundary conditions and introduce the reproducing kernel properties in which the initial conditions of the problem are satisfied. Based on reproducing kernel theory, reproducing kernel functions with a polynomial form will be constructed in the reproducing kernel spaces spanned by the generalized Jacobi basis polynomials. Some new error estimates for application of the method are established. The convergence analysis is established theoretically. The proposed method is successfully used for solving an option pricing problem arising in financial modelling. The ideas and techniques presented in this paper will be useful for solving many other problems.

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Section: Introductionmentioning

confidence: 99%

Generalized Jacobi Reproducing Kernel Method in Hilbert Spaces for Solving the Black-Scholes Option Pricing Problem Arising in Financial Modelling

Foroutan

Ebadian

Fazli

2018

Mathematical Modelling and Analysis

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“…Therefore, in this paper, the portfolio selection problem under fuzzy environment based on the constrained fuzzy optimization problem is going to be studied. Many modern computing methodologies can be seen for various fuzzy systems, for example, [8][9][10][11][12][13][14]. It is also worth mentioning that there are several results associated with parametric representations of fuzzy numbers [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Fard

Ramezanzadeh

2017

Complexity

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Fuzzy portfolio selection problem is a major issue in the financial field and a special case of constrained fuzzy-valued optimization problems (CFOPs). In this respect, the present paper aims to investigate the CFOP with regard to the features of the parametric representation of fuzzy numbers named as convex constraint function (CCF) which is proposed by Chalco-Cano et al. in 2014. Furthermore, relying on this parametric representation, some proper conditions are provided for the existence of solutions to a CFOP. To this end, by the increasing representation of CCF, the main problem is converted to a parametric multiobjective programming problem and some solution concepts from a similar framework in the multiobjective programming are proposed for the CFOP. Eventually to illustrate the proposed results, the fuzzy portfolio selection problem is discussed.

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“…Fuzzy differential equations (FDEs) are extensively used in modeling of complex phenomena arising in applied mathematics, physics, and engineering, including fuzzy control theory, quantum optics, atmosphere, measure theory and dynamical systems [1][2][3][4][5][6]. In many cases, data about these physical phenomena is pervaded under uncertainty, which may arise in the experiment part, data collection, measurement process as well as when determining the initial values.…”

Section: Introductionmentioning

confidence: 99%

Analytical treatment for solving system of fuzzy IVPs using residual power series approach

Aloroud¹

2017

imf

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The aim of the present analysis is present a relatively new analytical treatment, called residual power series (RPS) method, for solving system of fuzzy initial value problems under strongly generalized differentiability. The technique methodology provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. Several computational experiments are given to show the good performance and potentiality of the proposed procedure. The results reveal that the present simulated method is very effective, straightforward and powerful methodology to solve such fuzzy equations.

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Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Cited by 343 publications

References 52 publications

Generalized Jacobi Reproducing Kernel Method in Hilbert Spaces for Solving the Black-Scholes Option Pricing Problem Arising in Financial Modelling

Generalized Jacobi Reproducing Kernel Method in Hilbert Spaces for Solving the Black-Scholes Option Pricing Problem Arising in Financial Modelling

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Analytical treatment for solving system of fuzzy IVPs using residual power series approach

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