Some notes on convergence of homotopy based methods for functional equations
آ
عزیزی
دانشگاه پیام نور تهران
author
ج
سعیدیان
دانشگاه خوارزمی تهران
author
ا
بابلیان
دانشگاه خوارزمی تهران
author
text
article
2013
eng
Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizing previous works, a sucient condition for convergence ofhomotopy methods is presented. Finally, examples are given to show that evenif the homotopy method leads to a convergent series, it may not converge tothe exact solution of the equation under consideration.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
1
12
http://msj.iau-arak.ac.ir/article_514998_97009e58cebbe0cb936c4ac2ea5d7c14.pdf
Ranking DMUs by ideal points in the presence of fuzzy and ordinal data
م
ایزدیخواه
دانشگاه آزاد اراک
author
ز
علی اکبر پور
دانشگاه آزاد اراک
author
ه
شرفی
دانشگاه علوم و تحقیقات تهران
author
text
article
2013
eng
Envelopment Analysis (DEA) is a very eective method to evaluate the relative eciency of decision-making units (DMUs). DEA models divided all DMUs in two categories: ecient and inecientDMUs, and don't able to discriminant between ecient DMUs. On the other hand, the observedvalues of the input and output data in real-life problems are sometimes imprecise or vague, suchas interval data, ordinal data and fuzzy data. This paper develops a new ranking system under thecondition of constant returns to scale (CRS) in the presence of imprecise data, In other words, inthis paper, we reformulate the conventional ranking method by ideal point as an imprecise dataenvelopment analysis (DEA) problem, and propose a novel method for ranking the DMUs when theinputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose we convert alldata into interval data. In order to convert each fuzzy number into interval data we use the nearestweighted interval approximation of fuzzy numbers by applying the weighting function and also weconvert each ordinal data into interval one. By this manner we could convert all data into intervaldata. The numerical example illustrates the process of ranking all the DMUs in the presence of fuzzy,ordinal and interval data.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
13
36
http://msj.iau-arak.ac.ir/article_514999_5c7dc2f73150b39722dfb7edbec16b1b.pdf
Legendre wavelet method for solving Hammerstein integral equations of the second kind
ش
جوادی
دانشگاه خوارزمی تهران
author
ج
سعیدیان
دانشگاه خوارزمی تهران
author
ف
صفری
دانشکده ریاضی دانشگاه خوارزمی تهران
author
text
article
2013
eng
An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its superiority are presented.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
37
55
http://msj.iau-arak.ac.ir/article_515000_82910dddddcd079c95584dca6566e445.pdf
The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients
ز
خلته بجدی
دانشگاه بیرجند
author
س
احمدی اصل
دانشگاه بیرجند
author
ا
امین عطایی
دانشگاه خواجه نصیر الدین توسی تهران
author
text
article
2013
eng
In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierential equationsto solve a system of linear algebraic equations, thus greatly simplify the problem. In addition, severalnumerical experiments are given to demonstrate the validity and applicability of the method.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
57
80
http://msj.iau-arak.ac.ir/article_515001_cf35c3fcb35ec049ae5b367cc3365f0f.pdf
On the singular fuzzy linear system of equations
M
Nikuie
باشگاه پژوهشگران جوان دانشگاه آزاد یزد.
author
M.K.
Mirnia
Department of Computer engineering, Tabriz Branch, Islamic Azad
University, Tabriz, Iran.
author
text
article
2013
eng
The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
81
100
http://msj.iau-arak.ac.ir/article_515072_f39d05fb7b4b81f825ee5c5d92280b8b.pdf
Convergence Theorems for -Nonexpansive Mappings in CAT(0) Spaces
Savita
Rathee
هندوستان
author
R
Ritika
Department of Mathematics, M.D. University, Rohtak (Haryana), India
author
text
article
2013
eng
In this paper we derive convergence theorems for an -nonexpansive mappingof a nonempty closed and convex subset of a complete CAT(0) space for SP-iterative process and Thianwan's iterative process.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
101
114
http://msj.iau-arak.ac.ir/article_515073_2c90b18306b586d0c6a7ef5a9e2fd133.pdf
Numerical solution of fuzzy Hunter-Saxton equation by using Adomian decomposition and Homotopy analysis methods
ش.
صدیق بهزادی
Department of Mathematics, Islamic Azad University, Qazvin Branch,
Qazvin, Iran
author
text
article
2013
eng
In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical example is studied to demonstrate the accuracy ofthe presented methods.
In this paper, a fuzzy Hunter-Saxton equation is solved by using the Adomian'sdecomposition method (ADM) and homotopy analysis method (HAM). Theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. The existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. A numerical example is studied to demonstrate the accuracy ofthe presented methods.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
115
133
http://msj.iau-arak.ac.ir/article_515074_001127548a53e68b99a5049d12651104.pdf
Evaluating the solution for second kind nonlinear Volterra Fredholm integral equations using hybrid method
احمد
شهسواران
Islamic Azad University, Boroujerd Branch, Boroujerd, Iran.
author
اکبر
شهسواران
Islamic Azad University, Boroujerd Branch, Boroujerd, Iran.
author
text
article
2013
eng
In this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integral equations to the solution ofalgebraic equations. Finally, we also give some numerical examples that showsvalidity and applicability of the technique.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
135
149
http://msj.iau-arak.ac.ir/article_515075_93d04aac3c8e31dc1bd4cc309ecc4899.pdf
A note on positive deniteness and stability of interval matrices
H
Veiseh
Department of Applied Mathematics, Hamedan Branch, Islamic Azad
University, Hamedan, Iran
author
text
article
2013
eng
It is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive deniteness and stability of interval matricescan be presented. These conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.Furthermore we introduce a new necessary and sucient condition for checkingstability of interval matrices.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
151
158
http://msj.iau-arak.ac.ir/article_515076_fedf0dc7e74268bd7471f07d5e845be9.pdf
Multiple solutions of the nonlinear reaction-diusion model with fractional reaction
H.
Vosoughi
Department of Mathematics, Faculty of Science, Islamshahr Branch,
Islamic Azad University, Islamshahr, Tehran, Iran
author
E.
Shivanian
Department of Mathematics, Imam Khomeini International University,
Qazvin, 34149-16818, Iran
author
M.
Anbarloei
Department of Mathematics, Faculty of Science, Islamshahr Branch,
Islamic Azad University, Islamshahr, Tehran, Iran
author
text
article
2013
eng
The purpose of this letter is to revisit the nonlinear reaction-diusion modelin porous catalysts when reaction term is fractional function of the concen-tration distribution of the reactant. This model, which originates also in uidand solute transport in soft tissues and microvessels, has been recently givenanalytical solution in terms of Taylors series for dierent family of reactionterms. We apply the method so-called predictor homotopy analysis method(PHAM) which has been recently proposed to predict multiplicity of solutionsof nonlinear BVPs. Consequently, it is indicated that the problem for somevalues of the parameter admits multiple solutions. Also, error analysis of thesesolutions are given graphically.
Theory of Approximation and Applications
Islamic Azad University
2538-2217
9
v.
2
no.
2013
159
170
http://msj.iau-arak.ac.ir/article_515077_42386f352e68134a3980600013f1728c.pdf