| 第一类弱奇异核Fredholm积分方程的数值求解 |
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| 引用本文： | 闵涛,胡刚,晏立刚.第一类弱奇异核Fredholm积分方程的数值求解[J].应用泛函分析学报,2014(2):167-171. |
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| 作者姓名： | 闵涛 胡刚 晏立刚 |
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| 作者单位： | 西安理工大学理学院,西安710054 |
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| 基金项目： | 资助项目：国家自然科学基金重大项目（51190093）;国家自然科学基金（50979088,51179151） |
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| 摘 要： | 第一类弱奇异核Fredholm积分方程由于奇异及本质的不适定性，给求解带来很大难度．本文首先利用克雷斯变换将方程转化，并对转化后的方程进行高斯一勒让德离散，得到一离散不适定的线性方程组，结合正则化方法对该类问题进行数值求解．最后给出了数值模拟，验证了本文方法的可行性及有效性．
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| 关 键 词： | Fredholm积分方程 正则化 克雷斯变换 高斯-勒让德离散 |
A Numerical Solution of Weakly Singular Fredholm Integral Equation of First Kind |
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| MIN Tao,HU Gang,YAN Ligang.A Numerical Solution of Weakly Singular Fredholm Integral Equation of First Kind[J].Acta Analysis Functionalis Applicata,2014(2):167-171. |
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| Authors: | MIN Tao HU Gang YAN Ligang |
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| Institution: | (School of Sciences, Xi＇an University of Technology, Xi＇an 710054, China) |
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| Abstract: | Beacause the weakly singular Fredholm integral equation of first kind the nature of the singularity and ill-posedness, so solving is great difficulty. Then we firstly transform the equation into by Kress, and ransformed equations and Gauss-Legendre discrete, and we get the not be a discrete set of linear equations. Regularization method with the class of the numerical solution of the problem. Finally, a numerical simulation verify the feasibility and effectiveness. |
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| Keywords: | Fredholm integral equation regularization Kress transformation Gauss-Legendre |
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