On the Discretization Error of Parametized Nonlinear Equations,
Abstract
Many applications lead to nonlinear, parameter dependent equations H(y,t) = y sub o, where H: Y x T yields Y, y sub o epsilon rge H, and the state space Y is infinite-dimensional while the parameter space T has finite dimension. The case dim T = 1 is of special interest in connection with continuation methods. For this case, a general theory is developed which provides for the existence of solution paths of a rather general class of such equations and of their finite-dimensional approximations, and which allows for an assessment of the error between these paths. A principal tool in this analysis is the theory of nonlinear Fredholm operators. The results cover a more general class of operators than the mildly nonlinear mappings to which other approaches appear to be restricted. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1982
- Accession Number
- ADA120108
Entities
People
- James P. Fink
- Werner Rheinboldt
Organizations
- University of Pittsburgh