An AN-stable Rosenbrock-type method for solving stiff differential equations (Q1090080)

For the equation \(y'=\lambda (x)y\) the stability properties of Rosenbrock-Wanner (ROW) methods are investigated. It is shown that k- stage ROW-methods are not AN-stable for \(k\geq 2\). A second order improved ROW-method, which is AN-stable and with local error estimate is presented with some numerical results. The method is needed to be tested over a wide range of problems; the local truncation error must be estimated efficiently.