Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials
Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials
复制标题
DOI：
10.1137/0703055
复制
发表时间：
1966-12
影响因子：
2.9
通讯作者：
M. K. Miller;W. Guy
中科院分区：
文献类型：
--
作者：
M. K. Miller;W. Guy
函数f的泛函值由其在s的离散点处的拉普拉斯变换的值$F(s)$确定。在$s = (\beta + 1 + k)\delta ,\, k = 0,1, \cdots $给出的点处对$F(s)$的评估，以雅可比多项式的形式确定$f(t)$的无穷级数展开中的系数。$\beta $和$\delta $的值决定了沿实s轴计算$F(s)$的位置。利用$f(t)$的无穷级数展开的有限项，给出了$f(t)$的近似。给出了数值算例，并与目前已知的几种近似$f(t)$的数值方法进行了比较。
Functional values of a function f are determined from the values $F(s)$ of its Laplace transform at discrete points of s. Evaluation of $F(s)$ at points given by $s = (\beta + 1 + k)\delta ,\, k = 0,1, \cdots $, determine coefficients in an infinite series expansion of $f(t)$ in terms of Jacobi polynomials. The values of $\beta $ and $\delta $ determine the position along the real s-axis at which $F(s)$ is evaluated. An approximation to $f(t)$ is given by using a finite number of terms of the infinite series expansion of $f(t)$. Numerical examples are given and results are compared with some known numerical methods for approximating $f(t)$.