On the convergence of multistep methods for nonlinear stiff differential equations (Q806978)

This work concerns an application of the general linear multistep methods of the form \(\sum^{k}_{j=0}\alpha_ jy_{n+j}=h\sum^{k}_{j=0}\beta_ jf_{n+j}\) to numerical integration of nonlinear stiff problems. A nice general definition of stiffness and an elegant analysis of convergence of so called A(\(\alpha\))-stable algorithms of the discussed form create a basis for further applications. This general framework is applied to: a) Singularly perturbed first order systems of the form \(u'=a(u,v),\epsilon v=b(u,v),\) \(0<\epsilon \ll 1.\) b) Nonlinear parabolic problems. In my opinion this nice work marks a step forward in the theory of multistep methods for nonlinear stiff problems.