Stability and error estimates for the \(\theta\)-method for strongly monotone and infinitely stiff evolution equations (Q5944726)

The authors consider the well-known \(\theta\)-method for the equations named in the title and prove error estimates which are independent of the stiffness and show a convergence order between 1 and 2. By chosing the parameter \(\theta\) suitably near to \(1/2\), the order \(4/3\) is obtained without requiring special time step sequences nor differentiabilty of the right-hand operator. Second order is proved for nearly constant time steps. This results circumvent the order reduction phenomenon. The theoretical findings are also supported by several numerical experiments.