\(L\)-decremented ROW method of third-order accuracy (Q1975798)

A complete analysis of the three- and four-stage Rosenbrock-Wanner (ROW) methods is carried out. Families of schemes of third-order accuracy are obtained with the first and second order of \(L\)-decrementation of stiff components. A new algorithm is proposed for estimating the local error and for the automatic step control. Examples of specific schemes are presented. These schemes are compared with the best solver for the numerical solution of stiff systems of ordinary differential equations. The advantage of the \(L\)-decremented methods is demonstrated for a complicated test problem characterized by high stiffness (the Van der Pol nonlinear oscillator).