S. Abbasbandy
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14515/775, Iran.
[ 1 ] - A method for solving fully fuzzy linear system
In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...
[ 2 ] - Numerical Study of Unsteady Flow of Gas Through a Porous Medium By Means of Chebyshev Pseudo-Spectral Method
In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provi...
[ 3 ] - Numerical Simulation of 1D Linear Telegraph Equation With Variable Coefficients Using Meshless Local Radial Point Interpolation (MLRPI)
In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...
[ 4 ] - Application of the exact operational matrices for solving the Emden-Fowler equations, arising in Astrophysics
The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...
[ 5 ] - Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients
Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be solved?
[ 6 ] - The effects of MHD flow of third grade fluid by means of meshless local radial point interpolation (MLRPI)
The meshless local radial point interpolation (MLRPI) method is applied to examine the magnetohydrodynamic (MHD) ow of third grade uid in a porous medium. The uid saturates the porous space between the two boundaries. Several limiting cases of fundamental ows can be obtained as the special cases of present analysis. The variations of pertinent parameters are addressed.
[ 7 ] - The Ritz-Galerkin method for MHD Couette flow of non-Newtonian fluid
In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...
[ 8 ] - Interpolation of fuzzy data by using flat end fuzzy splines
In this paper, a new set of spline functions called ``Flat End Fuzzy Spline" is defined to interpolate given fuzzy data. Some important theorems on these splines together with their existence and uniqueness properties are discussed. Then numerical examples are presented to illustrate the differences between of using our spline and other interpolations that have been studied before.
[ 9 ] - A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers
Fuzzy measures are suitable in analyzing human subjective evaluation processes. Several different strategies have been proposed for distance of fuzzy numbers. The distances introduced for fuzzy numbers can be categorized in two groups:\1. The crisp distances which explain crisp values for the distance between two fuzzy numbers.\2. The fuzzy distance which introduce a fuzzy distance for normal f...
[ 10 ] - Fuzzy collocation methods for second- order fuzzy Abel-Volterra integro-differential equations
In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.
[ 11 ] - REVISION OF SIGN DISTANCE METHOD FOR RANKING OF FUZZY NUMBERS
Recently, Abbasbandy and Asady have been proposed a modificationof the distance based approach, namely ``sign distance method''.However, in this paper, it is shown that this method has some drawbacks, i.e.,the result is not consistent with human intuition for specialcases and this method cannot always logically infer rankingorder of the images of the fuzzy numbers. In this paper, wepresent a re...
[ 12 ] - NEW RESULTS ON THE EXISTING FUZZY DISTANCE MEASURES
In this paper, we investigate the properties of some recently pro-posed fuzzy distance measures. We find out some shortcomings for these dis-tances and then the obtained results are illustrated by solving several examplesand compared with the other fuzzy distances.
[ 13 ] - gH-differentiable of the 2th-order functions interpolating
Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...
[ 14 ] - An Efficient Numerical Method for a Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme
We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...
[ 15 ] - Multiple solutions of a nonlinear reactive transport model using least square pseudo-spectral collocation method
The recognition and the calculation of all branches of solutions of the nonlinear boundary value problems is difficult obviously. The complexity of this issue goes back to the being nonlinearity of the problem. Regarding this matter, this paper considers steady state reactive transport model which does not have exact closed-form solution and discovers existence of dual or triple solutions in so...
[ 16 ] - The use of radial basis functions by variable shape parameter for solving partial differential equations
In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...
[ 17 ] - An Effective Numerical Technique for Solving Second Order Linear Two-Point Boundary Value Problems with Deviating Argument
Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...
[ 18 ] - The fuzzy generalized Taylor’s expansion with application in fractional differential equations
In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...
[ 19 ] - Homotopy analysis method and its application for singularly perturbed delay differential equations with layer behavior
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