The Approximate Solution of Nonlinear Fixed Point Operator Equations in Normed Linear Spaces.
TEXAS UNIV AUSTIN ELECTRONICS RESEARCH CENTER
Pagination or Media Count:
The report presents a class of new algorithms for the approximate determination of the fixed points of operators in normed linear spaces. The method of averaging functional corrections is itself a generalization of the classical method of successive approximations. Theoretical results concerning the convergence characteristics of the new algorithms are presented. The new methods are shown to be superior to the method of averaging functional corrections for certain types of operators. The primary application is to boundary value problems in integral equation form, and the representation of boundary value problems in this form is discussed. Other potential practical applications are considered. Numerical examples are given which demonstrate that the new algorithms are computational methods of significant practical value. Author
- Theoretical Mathematics