Taylor series

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1 - High level Ab inito bench mark computaions on weak interactions (H2)2 dimer revisited
G.H. Shafiee A. Sadjadi Seik Weng Ng

The Potential Energy Surface PES of (H2)2 dimer has been investigated, using five simple rigid rotor models. These models are called: head to head, symmetric side to side, L , steplike and T model. All calculations were done at two levels of ab initio methods: MP2(Full) أکثر

The Potential Energy Surface PES of (H2)2 dimer has been investigated, using five simple rigid rotor models. These models are called: head to head, symmetric side to side, L , steplike and T model. All calculations were done at two levels of ab initio methods: MP2(Full) and QCISD (T,Full) using cc-pVTZ basis set at singlet state of spin multiplicity. The results of scanning PES were then fitted to Taylor series up to 15 terms to obtain the equilibrium distances and interaction energies between pairs of H2 molecules.The standard deviation of the residuals in fitting procedure is well below 10-9 in all cases.L model has been found to be the most stable one instead of previously reported T model and 7 times more stable than other models.The validity of hard sphere approximation was also tested by solving simple mathematical equation and found to be no longer valid in these interactions. تفاصيل المقالة

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2 - The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential ‎Equations
A. Alvandi M. Paripour

&lrm;This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo \cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproduc أکثر

&lrm;This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo \cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by using Taylor series. Some numerical examples are studied to demonstrate the accuracy of the given &lrm;method.&lrm; تفاصيل المقالة

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3 - Approximate solution of the stochastic Volterra integral equations via expansion method
M. Khodabin K. Maleknejad T. Damercheli

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which أکثر

In this paper, we present an efficient method for determining the solution of the stochastic second kind Volterra integral equations (SVIE) by using the Taylor expansion method. This method transforms the SVIE to a linear stochastic ordinary differential equation which needs specified boundary conditions. For determining boundary conditions, we use the integration technique. This technique gives an approximate simple and closed form solution for the SVIE. Expectation of the approximating process is computed. Some numerical examples are used to illustrate the accuracy of the method. تفاصيل المقالة

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4 - Computational technique of linear partial differential equations by reduced differential transform ‎method
H. &lrm;Rouhparvar&lrm;

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calcu أکثر

This paper presents a class of theoretical and iterative method for linear partial differential equations. An algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. In this technique, the solution is calculated in the form of a series with easily computable components. There test modeling problems from mathematical mechanic, physic, electronic and so on, and are discussed to illustrate the effectiveness and the performance of the our &lrm;method. تفاصيل المقالة

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5 - Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and Second Kind
Ahmad Shahsavaran M. M. Shamivand

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interva أکثر

In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which leads to approximating the unknown function and it's derivatives in terms of Chebyshev polynomials of the first kind. The proposed method, transforms the Abel's integral equations of the first and second kind into a system of linear algebraic equations which can be solved by Gaussian elimination algorithm. Finally, some numerical examples are included to clarify the accuracy and applicability of the presented method which indicate that proposed method is computationally very attractive. In thispaper, all numerical computations were carried out on a PC executing some programs written in maple software. تفاصيل المقالة

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6 - Analytical solution of the Hunter-Saxton equation using the reduced dierential transform method
H. Rouhparvar

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear أکثر

In this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the Hunter-Saxton equation. The main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. It is a semi analytical-numerical method that formulizes Taylor series in a very dierent manner.The numerical results denote that reduced dierential transform method isecient and accurate for Hunter-Saxton equation. تفاصيل المقالة

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7 - A Novel High-Order Fuzzy Systems with ‎Decomposition in to Zero-and First-Order Fuzzy ‎Structures in Nonlinear Dynamic Systems
Zohreh Zeighami Mohammad Reza Jahed Motlag Ali Moarefianpour

Fuzzy modeling is a relatively new system modeling method with a proven efficiency record in various fields. Although zero- and first-order fuzzy systems are common due to their simplicity, their linear structure faces challenges when modeling nonlinear systems with sta أکثر

Fuzzy modeling is a relatively new system modeling method with a proven efficiency record in various fields. Although zero- and first-order fuzzy systems are common due to their simplicity, their linear structure faces challenges when modeling nonlinear systems with state-variable interaction. These challenges include an increase in the number of rules and the inability to stabilize highly nonlinear systems. One solution is to use high-order fuzzy systems, which have a nonlinear structure and can represent model input interactions. In previous research, high-order fuzzy modeling has been investigated for static and nonlinear systems based on data, but such modeling has not been applied to dynamic systems with nonlinear nature which is a model of industrial processes. The present paper proposes a novel fuzzy structure inspired by the Taylor series expansion for dynamic systems with nonlinear state-space equations. This structure has a high degree of freedom in modeling complex nonlinear processes and can be adapted to the state-space equations of the system. The main novelty of this method is the conversion of a nonlinear high-order fuzzy structure into a set of first-order fuzzy structures. Another advantage is the ability to calculate the coefficients of the high-order fuzzy system from the Taylor series coefficients of the dynamic system’s model. Fuzzy systems have made various applications possible in the field of approximation. The present paper also proves the approximation ability and convergence of the proposed structure and determines its convergence criteria. تفاصيل المقالة

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8 - Tracking Control of Robots Revisited Based on Taylor Series and Asymptotic Expansion
Ali Deylami

This paper points out some errors based on the one-dimensional Taylor series for a multi-dimensional function that is used for robots manufacturing. It is argued that the proof of theorem 1 is not mathematically true, and consequently, the obtained results cannot be cor أکثر

This paper points out some errors based on the one-dimensional Taylor series for a multi-dimensional function that is used for robots manufacturing. It is argued that the proof of theorem 1 is not mathematically true, and consequently, the obtained results cannot be correct. In addition to this, the stability analysis presented in the paper does not address the saturated area properly. Therein, stability is analyzed separately in saturated and unsaturated operation areas. However, the stability of the closed-loop system may not be guaranteed through these separate analyses, since transitions from saturation area to unsaturated area and vice versa are neglected. This work is an extension of the above paper, based on the revised Taylor series and considering actuator saturation limit in both controller design and stability analysis. تفاصيل المقالة

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9 - An iterative method for forecasting most probable point of stochastic demand
J. Behnamian S. M. T. Fatemi Ghomi B. Karimi M. Fadaei Moludi

The demand forecasting is essential for all production and non-production systems. However, nowadays there are only few researches on this area. Most of researches somehow benefited from simulation in the conditions of demand uncertainty. But this paper presents an أکثر

The demand forecasting is essential for all production and non-production systems. However, nowadays there are only few researches on this area. Most of researches somehow benefited from simulation in the conditions of demand uncertainty. But this paper presents an iterative method to find most probable stochastic demand point with normally distributed and independent variables of n-dimensional space and the demand space is a nonlinear function. So this point is compatible with both external conditions and historical data and it is the shortest distance from origin to the approximated demand-state surface. Another advantage of this paper is considering ndimensional and nonlinear (nth degree) demand function. Numerical results proved this procedure is convergent and running time is reasonable. تفاصيل المقالة

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10 - Solving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
M. Karimian

In this study we produced a new method for solving regular differential equationswith step size h and Taylor series. This method analyzes a regular differential equation withinitial values and step size h. this types of equations include quadratic and cubic homogenouseq أکثر

In this study we produced a new method for solving regular differential equationswith step size h and Taylor series. This method analyzes a regular differential equation withinitial values and step size h. this types of equations include quadratic and cubic homogenousequations with constant coeffcients and cubic and second-level equations. تفاصيل المقالة

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11 - NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
Ahmad Shahsavaran Akbar Shahsavaran Forough Fotros

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the أکثر

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given. تفاصيل المقالة

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12 - A TAYLOR SERIES APPROACH FOR SOLVING LINEAR FRACTIONAL DECENTRALIZED BI-LEVEL MULTI-OBJECTIVE DECISION-MAKING UNDER FUZZINESS
Mansour Saraj Nima Safaei

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approa أکثر

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approach, the membership functions associated with each objective(s) ofthe level(s) of LFDBL-MODM are transformed by using a Taylor series and then they areunified. On using the Kuhn-Tucker conditions, the problem is finally reduced to a singleobjective. Numerical example is given in order to illustrate the efficiency and superiorityof the proposed approach. تفاصيل المقالة

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13 - A HOMOTOPY PERTURBATION ALGORITHM AND TAYLOR SERIES EXPANSION METHOD TO SOLVE A SYSTEM OF SECOND KIND FREDHOLM INTEGRAL EQUATIONS
S. M. Mirzaei

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equa أکثر

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary diﬀerential equation. تفاصيل المقالة

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14 - AN ANALYTICAL SOLUTION FOR DIFFUSION AND NONLINEAR UPTAKE OF OXYGEN IN THE RETINA
Deepti Seth

A simple mathematical model of steady state oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. The approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. أکثر

A simple mathematical model of steady state oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. The approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. The computational results for the scaled variables are presented through graphs. The effect of the important parameters (1) diffusion coefficient (2) metabolic rate constant (3) retinal capillary concentration are examined and discussed. تفاصيل المقالة

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15 - NUMERICAL SOLUTION OF THE MOST GENERAL NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL-DIFFERENCE EQUATIONS BY USING TAYLOR POLYNOMIAL APPROACH
H. Adibi A. Taherian

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix eq أکثر

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the method by numerical examples تفاصيل المقالة

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