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Operational Tau approximation for a general class of fractional integro-differential equations
Vanani, S. Karimi;Aminataei, A.;
Computational & Applied Mathematics , 2011, DOI: 10.1590/S1807-03022011000300010
Abstract: in this work, an extension of the algebraic formulation of the operational tau method (otm) for the numerical solution of the linear and nonlinear fractional integro-differential equations (fides) is proposed. the main idea behind the otm is to convert the fractional differential and integral parts of the desired fide to some operational matrices. then the fide reduces to a set of algebraic equations. we demonstrate the tau matrix representation for solving fides based on arbitrary orthogonal polynomials. some advantages of using the method, errorestimation and computer algorithm are also presented. illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. mathematical subject classification: 65m70, 34a25, 26a33, 47gxx.
A General Three-Step Class of Optimal Iterations for Nonlinear Equations
Fazlollah Soleymani,Solat Karimi Vanani,Abtin Afghani
Mathematical Problems in Engineering , 2011, DOI: 10.1155/2011/469512
Abstract: Many of the engineering problems are reduced to solve a nonlinear equation numerically, and as a result, an especial attention to suggest efficient and accurate root solvers is given in literature. Inspired and motivated by the research going on in this area, this paper establishes an efficient general class of root solvers, where per computing step, three evaluations of the function and one evaluation of the first-order derivative are used to achieve the optimal order of convergence eight. The without-memory methods from the developed class possess the optimal efficiency index 1.682. In order to show the applicability and validity of the class, some numerical examples are discussed.
A Low-cost Numerical Algorithm for the Solution of Nonlinear Delay Boundary Integral Equations
S. Karimi Vanani,S. Heidari,M. Avaji
Journal of Applied Sciences , 2011,
Abstract: Telescoping Decomposition Method (TDM) as a new modification of the well-known Adomian Decomposition Method (ADM) for solving Delay Boundaries Integral Equations (DBIEs) is presented. The proposed method yields an iterative algorithm to obtain the numerical and analytical solutions of DBIEs including linear and nonlinear terms. The main characteristic of the proposed method is to avoid calculating the Adomian polynomials and yields a simple algorithm. In the obtained algorithm, some orthogonal polynomials are effectively implemented to achieve better approximation for the nonhomogeneous and nonlinear terms that leads to facilitate the computational work. Some illustrative linear and nonlinear experiments are given to show the capability and validity of the proposed algorithm.
A Class of Three-Step Derivative-Free Root Solvers with Optimal Convergence Order
F. Soleymani,S. Karimi Vanani,M. Jamali Paghaleh
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/568740
Abstract: A class of three-step eighth-order root solvers is constructed in this study. Our aim is fulfilled by using an interpolatory rational function in the third step of a three-step cycle. Each method of the class reaches the optimal efficiency index according to the Kung-Traub conjecture concerning multipoint iterative methods without memory. Moreover, the class is free from derivative calculation per full iteration, which is important in engineering problems. One method of the class is established analytically. To test the derived methods from the class, we apply them to a lot of nonlinear scalar equations. Numerical examples suggest that the novel class of derivative-free methods is better than the existing methods of the same type in the literature.
On the coupling of homotopy perturbation and Laplace transformation for system of partial differential equations
M. Khan,M. A. Gondal,S. Karimi Vanani
Applied Mathematical Sciences , 2012,
Abstract:
Operational Tau Approximation for Neutral Delay Differential Systems
J. Sedighi Hafshejani,S. Karimi Vanani,J. Esmaily
Journal of Applied Sciences , 2011,
Abstract: Neutral Delay Differential Systems (NDDSs) arise in many areas of various mathematical modeling. Infectious diseases, population dynamics, physiological and pharmaceutical kinetics and chemical kinetics, the navigational control of ships and mechanical systems, chemical process simulation and optimal control are the main field concerning with NDDSs. The purpose of this study was to present an extension of the algebraic formulation of the Operational Tau Method (OTM) for the numerical solution of NDDSs. The proposed method converts the delay parts of the desired NDDS to some operational matrices. Then the NDDS reduces to a set of algebraic equations. Some orthogonal bases including shift Chebyshev and shifted Legendre polynomials are used to decrease the volume of computations. Two illustrative linear and nonlinear experiments are included to show the high accuracy and efficiency of the proposed method.
Study of Photocatalytic Behavior of Photochemical Doped TiO2 Nanoparticles with In-V Synthesized by Sol-gel and Hydrothermal Methods
Hamadanian Khozani M.,Reisi-Vanani A.,Razi P.,Hoseinifard S.
Proceedings of the International Conference Nanomaterials : Applications and Properties , 2012,
Abstract: Indium- vanadium doped with different molar percent (0.05-1%) was prepared by photochemical reduction method on pure TiO2 nanoparticles synthesized by sol –gel and hydrothermal process. XRD, FT-IR, TEM, SEM and EDX analysis were done for characterized nanoparticles and methyl orange (MO) was used as an environmental pollutant to verify photocatalytic effect of synthesized particles under visible and UV lamps. Result of tests was showed that In-V doping restrain from crystal growth, that only hydrothermal TiO2 particles with binary doped 0.2% molar of In-V can improve photocatalytic activity compared to sol-gel nanoparticles. Pure TiO2 prepared by hydrothermal and sol-gel processes were calcined at 300,400,450,550 oC for 3h and 500o C for 2h, respectively.
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