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Iterative-Collocation Method for Integral Equations of Heat Conduction Problems

机译:导热问题积分方程的迭代协调配置方法

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The integral equations studied here play very important role in the theory of parabolic initial-boundary value problems (heat conduction problems) and in various physical, technological and biological problems (epidemiology problems). This paper is concerned with the iterative-collocation method for solving these equations. We propose an iterative method with corrections based on the interpolation polynomial of spatial variable of the Lagrange type with given collocation points. The coefficients of these corrections can be determined by a system of Volterra integral equations. The convergence of the presented algorithm is proved and an error estimate is established. The presented theory is illustrated by numerical examples and a comparison is made with other methods.
机译:在此研究的积分方程在抛物线初值问题(热传导问题)和各种物理,技术和生物学问题(流行病学问题)的理论中起着非常重要的作用。本文涉及求解这些方程的迭代配置方法。我们基于给定搭配点的Lagrange类型空间变量的插值多项​​式,提出了一种带有修正的迭代方法。这些校正的系数可以通过Volterra积分方程系统确定。证明了所提算法的收敛性,并建立了误差估计。通过数值例子说明了提出的理论,并与其他方法进行了比较。

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