Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems

M. Heydari; Z. Avazzadeh; H. Navabpour; G.B. Loghmani

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Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems

机译：第二类Fredholm积分方程的积分平均值定理II的数值解。高维问题

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摘要

In this work, we generalize the numerical method discussed in [Z. Avazzadeh, M. Heydari, G.B. Loghmani, Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem, Appl. math, modelling, 35 (2011) 2374-2383] for solving linear and nonlinear Fredholm integral and integro-differential equations of the second kind. The presented method can be used for solving integral equations in high dimensions. In this work, we describe the integral mean value method (IMVM) as the technical algorithm for solving high dimensional integral equations. The main idea in this method is applying the integral mean value theorem. However the mean value theorem is valid for multiple integrals, we apply one dimensional integral mean value theorem directly to fulfill required linearly independent equations. We solve some examples to investigate the applicability and simplicity of the method. The numerical results confirm that the method is efficient and simple.

机译：在这项工作中，我们推广了[Z.]中讨论的数值方法。 Avazzadeh，M.Heydari，G.B. Loghmani，第二类Fredholm积分方程的数值解，使用积分平均值定理Appl。 Math，modelling，35（2011）2374-2383]，用于求解第二类线性和非线性Fredholm积分方程和积分微分方程。所提出的方法可以用于求解高维积分方程。在这项工作中，我们将积分均值方法（IMVM）描述为解决高维积分方程的技术算法。该方法的主要思想是应用积分平均值定理。但是，平均值定理对多个积分有效，我们直接应用一维积分平均值定理来满足所需的线性独立方程。我们解决了一些例子，以研究该方法的适用性和简便性。数值结果证实了该方法的有效性和简便性。

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来源
《Applied Mathematical Modelling》 |2013年第2期|432-442|共11页
作者
M. Heydari; Z. Avazzadeh; H. Navabpour; G.B. Loghmani;
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作者单位

Department of Mathematics, Yazd University, P.O. Box 89195-741 Yazd, Iran;

Department of Mathematics, Yazd University, P.O. Box 89195-741 Yazd, Iran;

Department of Mathematics, Yazd University, P.O. Box 89195-741 Yazd, Iran;

Department of Mathematics, Yazd University, P.O. Box 89195-741 Yazd, Iran;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
integral mean value theorem; fredholm integral equations; multiple integral equations; systems of integral equations;

机译：积分中值定理;弗雷德霍尔姆积分方程;多个积分方程;积分方程组;

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1. Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem [J] . Z. Avazzadeh, M. Heydari, G.B. Loghmani Applied Mathematical Modelling . 2011,第5期

机译：第二类Fredholm积分方程的积分均值定理数值解
2. Numerical solution for three-dimensional nonlinear mixed Volterra-Fredholm integral equations via three-dimensional block-pulse functions [J] . Farshid Mirzaee, Elham Hadadiyan, Saeed Bimesl Applied mathematics and computation . 2014,第Null期

机译：基于三维块脉冲函数的三维非线性混合Volterra-Fredholm积分方程的数值解
3. Numerical solution of the linear two-dimensional Fredholm integral equations of the second kind via two-dimensional triangular orthogonal functions [J] . Farshid Mirzaee, Sima Piroozfar Journal of King Saud University . 2010,第4期

机译：第二类线性二维弗雷德霍尔姆积分方程的二维三角正交函数数值解
4. Numerical solution of stochastic mixed Volterra-Fredholm integral equations driven by space-time Brownian motion via two-dimensional block pulse functions [C] . Farkhondeh Hosseini Shekarabi, Tayebeh Damercheli International Conference on Analysis and Applied Mathematics . 2018

机译：天空时间褐色运动通过二维块脉冲函数驱动的随机混合Volterra-Fredholm积分方程的数值解
5. THE NUMERICAL SOLUTION OF LINEAR FIRST KIND FREDHOLM INTEGRAL EQUATIONS USING AN ITERATIVE METHOD [D] . SCHMIDT, ROBERT CRAIG 1987

机译：线性一类Fredholm积分方程的迭代法数值解
6. Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem [O] . Ahmet Altürk -1

机译：线性和非线性Fredholm积分方程的加权均值定理数值解
7. Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems [O] . Heydari M., Avazzadeh Z., Navabpour H., 2013

机译：第二类Fredholm积分方程的积分平均值定理II的数值解。高维问题

Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem II. High dimensional problems

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