Application and Numerical Solution of Abel-Type Integral Equations.
Abstract
This paper reviews the numerous applications in which the solution of equations like the Abel-type integral equation for discrete observational data (d sub i) is the basic step, compares, with respect to given discrete observational data (d sub i), the use of pseudo-analytic methods and the direct evaluation of its inversion formulas as a basis for solving this equation, proposes a specific algorithm based on these conclusions, and examines the consequences of the fact that, for the equation, linear functionals defined on its solution u(x) can be redefined as linear functionals on the data s(y). The justification for the latter is that, in applications involving separable first kind Abel-type integral equations, inferences are usually based on (linear) functionals defined on u(x), not on u(x) itself. This point is illustrated with an example from metallurgy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1977
- Accession Number
- ADA049396
Entities
People
- R. S. Anderssen
Organizations
- University of Wisconsin–Madison