| L~1空间带弱奇异核的第二类Fredholm积分方程解法探究 |
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| 引用本文： | 王婧宜,王辉,张欣.L~1空间带弱奇异核的第二类Fredholm积分方程解法探究[J].数学的实践与认识,2014(12). |
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| 作者姓名： | 王婧宜 王辉 张欣 |
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| 作者单位： | 哈尔滨师范大学数学科学学院;中国科学院数学与系统科学研究院; |
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| 基金项目： | 黑龙江省教育厅科学技术研究项目(12521145) |
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| 摘 要： | 针对带有弱奇异核的第二类Fredholm积分方程数值解法问题,介绍了两种方法.一种方法是直接用L~1空间中的离散化方法求其数值解;另一种方法是将弱奇异核通过迭代变为连续核,再用L~1空间中的离散化方法求其数值解,且通过对具体算例作图分析,从而得出直接用L~1空间中离散化方法更好.
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| 关 键 词： | Fredholm积分方程 弱奇异核 连续核 离散化方法 误差估计 |
Explore the Discretization Method with Weakly Singular Kernel Fredholm Integral Equation of the Second Kind |
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| Abstract: | According to the second kinds of Fredholm with weakly singular integral equation method for the numerical solution of the problem,introduces two methods.One method is the direct use of the discretization method in one dimension space and its numerical solution is obtained;another method is to weakly singular kernel through iterative into continuous nuclear,to calculate the numerical solution of one-dimensional discretization method and in space,and through the concrete example mapping analysis,so that a better discretization method in one dimension. |
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| Keywords: | fredholm integral equation weakly singular kernel continuous kernel discretization method taylor series expansion error estimates |
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