Spline Approximation to the Solution of a Class of Abel Integral Equations.
Abstract
Global approximation methods for solving the Abel integral equation by means of splines with full continuity are considered. The methods are based on using the differentiated form of the above equation. It is shown that the use of linear splines in C leads to a 2-alpha method for 0 < alpha < 1 and the use of quadratic splines in C1 leads to a 3-alpha method, which computational experiments indicate is stable for 0 < alpha < 1. The same technique applied to cubic and higher-order splines gives rise to divergent methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1979
- Accession Number
- ADA068944
Entities
People
- Hing-sum Hung
Organizations
- University of Wisconsin–Madison