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Summary.   For evolution equations with a strongly monotone operator  we derive unconditional stability and discretization error estimates valid for all . For the -method, with , we prove an error estimate , if , where  is the maximal integration step for an arbitrary choice of sequence of steps and with no assumptions about the existence of the Jacobian as well as other derivatives of the operator , and an optimal estimate  under some additional relation between neighboring steps. The first result is an improvement over the implicit midpoint method , for which an order reduction to  sometimes may occur for infinitely stiff problems. Numerical tests illustrate the results.

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