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带弱奇异核的第二类Fredholm积分方程数值解法比较
Comparison of Numerical Solutions for the Second Kind Fredholm Integral Equation with Weakly Singular Kernel
【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.一种方法是泰勒级数展开法;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L~1空间中离散化方法更好.
【Abstract】 There are two kinds of methods to find the numerical solution for the second kind Fredholm integral equation with weakly singular kernel.One is the Taylor series expansion method.Another method is that we transform weakly singular kernel into continuous kernel, and then use the discretization method for the numerical solution in L~1 space,and analysis a specific example by mapping to arrive at the discretization method from L~1 space is better.
【关键词】 Fredholm积分方程;
弱奇异核;
连续核;
离散化方法;
泰勒级数展开;
误差估计;
【Key words】 fredholm integral equation; weakly singular kernel; continuous kernel; discretization method; taylor series expansion; error estimates;
【Key words】 fredholm integral equation; weakly singular kernel; continuous kernel; discretization method; taylor series expansion; error estimates;
【基金】 黑龙江省教育厅科学技术研究项目(12521145)
- 【文献出处】 数学的实践与认识 ,Mathematics in Practice and Theory , 编辑部邮箱 ,2013年22期
- 【分类号】O241.83
- 【被引频次】5
- 【下载频次】134