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Journal Paper

Approximation of Parametric Curves by Moving Least Squares Method

Applied Mathematics and Computation, Vol. 283, (2016) 290-298.

In this work we propose a method to approximate a parametric curve in . Some distinct points in  are given, we assume that these points belong to a parametric curve and our aim is to approximate these data by Moving Least Squares method. We mention several applications of the proposed method to emphasize the importance of the work, also Root Mean Squares errors and Hausdorff distances between the exact curve and its approximation are presented to demonstrate the efficiency and reliability of the method.

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Journal Paper

Solving Linear Partial Differential Equations by Moving Least Squares Method

Bulletin of the Georgian National Academy of Sciences, Vol. 9, No. 3, (2015) 26-36.

In this work we consider a method for solving linear partial differential equations, specially heat and waves equations that describe behavior of temperature distribution and wave propagation in one or multidimensional environments by moving least squares procedure. We present some illustrative examples and compare our proposed method with other methods to show the efficiency of this method.

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Journal Paper

Interpolation by Xuli type Operators Based on Linear B-Splines

Journal of Interpolation and Approximation in Scientific Computing, 2015 No.1 (2015) 9-19.

In this paper we use modified Taylor expansion of order $r$ on spline functions of degrees 0 and 1 to present two Xuli-type operators. Errors of the new operators are analyzed and they are compared with Hermite interpolation operator which uses the same data. Finally the efficiency of this method is shown by presenting some illustrative examples.

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conference paper

Solving Fredholm Integral Equations by Discrete Least Squares Method

44th Annual Iranian Mathematics Conference, (AIMC44) (2013), Ferdowsi University of Mashhad, Iran.

In this paper we use Discrete Least Squares Method (DLSM )to solve Fredholm Integral Equations. In this method we take $n+1$ distinct points on interval $[a,b]$ and we apply discrete norm 2 for the residual function, in this case the computations is relatively simple and straightforward in comparing to Least Squares Method (LSM) also the error of DLSM will be smaller than the error of LSM. We present some illustrative examples to show the efficiency of this method.

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