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
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.
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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.
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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.
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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.
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