刘玲,杨镇.第一类卷积型Volterra积分方程的快速配置边值方法[J].重庆工商大学学报(自然科学版),2020,37(4):83-88
LIU Ling,YANG Zhen.Fast Collocation Boundary Value Method for Convolution type Volterra Integral Equation of the First Kind[J].Journal of Chongqing Technology and Business University(Natural Science Edition),2020,37(4):83-88
第一类卷积型Volterra积分方程的快速配置边值方法
Fast Collocation Boundary Value Method for Convolution type Volterra Integral Equation of the First Kind
  
DOI:
中文关键词:  Volterra 积分方程  配置边值法  Toeplitz 矩阵  快速Fourier 变换
英文关键词:Volterra integral equation  collocation boundary value method  Toeplitz matrix  fast Fourier transform.
基金项目:
作者单位
刘玲,杨镇 贵州大学 数学与统计学院, 贵阳 550025 
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中文摘要:
      针对第一类卷积型Volterra积分方程的数值解,研究其快速算法;基于特殊的多步配置方法,利用未计算的近似值,构造了高阶数值格式;通过格式,将原积分方程离散为线性方程组,其中系数矩阵可分解为Toeplitz矩阵和稀疏矩阵;利用快速Fourier变换计算该线性方程组,运算量为O(Nlong N);数值例子验证了方法的高效性。
英文摘要:
      This paper is devoted to studying the fast numerical method for convolution type Volterra integral equation of the first kind. High order numerical schemes are devised by using special multi step collocation methods, which depend on numerical approximations of the solution in the next several steps. Then the original integral equation is discretized into a system of linear equations, and the coefficient matrix can be decomposed into a Toeplitz matrix and a sparse matrix. The fast calculation of linear equations is implemented by using fast Fourier transform in this paper, and the calculation amount is O(NlogN). Numerical examples are provided to demonstrate the efficiency of the proposed method.
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