Stability analysis of one-leg methods for nonlinear functional differential and functional equations
The aim of this paper is to deal with the numerical methods for a nonlinear system \[ \begin{aligned} y'(t) & = f(t,y(t), y(t-\tau), z(t-\tau))\\ z'(t) & = g(t,y(t), y(t-\tau), z(t-\tau)), t\geq 0 \end{aligned} \] The adaptation of one-leg method is considered for solving systems of nonlinear functional differential and functional equations. It is proved that an \(A\)-stable one-leg method is globally stable and a strongly \(A\)-stable one-leg method is asymptotically stable under suitable conditions. A numerical example is considered to illustrate these results.
nonlinear functional differential and functional equations
scientific article; zbMATH DE number 5798201
scientific article