Inexact methods in the numerical solution of stiff initial value problems (Q1969308)

The paper deals with the analysis of the local convergence properties of the inexact Newton methods (IN-methods) which can be effectively used for solving large stiff initial value problems for nonlinear ordinary differential equations. New conditions assuring linear convergence of IN-methods in terms of a sequence of forcing terms uniformly less than one and for an arbitrary consistent norm are established and a new stopping criterion for the inner iterations is proposed. Numerical experiments with LSODEIN - the modification of the code LSODE based on the backward differentiation formulas - are reported and the robustness, reliability and effectiveness of the proposed modifications of LSODE are discussed in comparison with those of the original code.