Numerical and Approximate Methods for The One-Dimensional Inverse Scattering Problem

Ge De-biao

您当前的位置：

首页 >

文章列表页 >

Numerical and Approximate Methods for The One-Dimensional Inverse Scattering Problem

更新时间：2025-12-08

- Numerical and Approximate Methods for The One-Dimensional Inverse Scattering Problem
- Acta Electronica Sinica Issue 5, Pages: 32-37(1983)
- 作者机构：
  
  1. 西北电讯工程学院
  2. University of Pennsylvania
  3. 西北电讯工程学院University of Pennsylvania
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：1983
- 稿件说明：
移动端阅览
[1]葛德彪,H.N.Kritikos,D.L.Jaggard.一维逆散射问题的数值解法及近似解法[J].电子学报,1983(05):32-37.

Ge De-biao. Numerical and Approximate Methods for The One-Dimensional Inverse Scattering Problem[J]. Acta Electronica Sinica, 1983, (5): 32-37.
[1]葛德彪,H.N.Kritikos,D.L.Jaggard.一维逆散射问题的数值解法及近似解法[J].电子学报,1983(05):32-37. DOI：

Ge De-biao. Numerical and Approximate Methods for The One-Dimensional Inverse Scattering Problem[J]. Acta Electronica Sinica, 1983, (5): 32-37. DOI：

摘要

一维逆散射问题

本世纪中期已归结为求解Gel’fand-Levitan积分方程的问题

其在某些情况下的解析解已经获得。本文研究两种不同的方法。其一为迭代蛙跃法

即用数值方法求解积分方程。实际计算表明

此法简明而有效。另一为Born近似方法

它给出了解析表达式

由此可重建分界面附近一定区域的势函数。文中用这两种方法讨论了若干例子。

Abstract

The one-dimensional inverse scattering problem has been reduced to the solution of an integral equation by the pioneering work of Gel’fand and Levitan

circa 1950. To date

closed form solutions to this problem have been obtained for a limited class of scattered data. We investigate two alternative approaches. The first technique involves leapfrogging in space and time to numerically solve the desired integral equation for many classes of scattering data. This novel method is simple and efficient. The second technique provides an approximate reconstruction under appropriate restrictions. Both methods are demonstrated with several examples.

关键词

Keywords

references

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰