Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
For evolution equation with a monotone operator we derive unconditional stability and error estimates valid for all times. θ-method, For the θ=1/2(2+ζτV), 0<v≤1, ζ>0), we prove an error estimate O(τ4/3), τ → 0, if V=1/3, where τ is the maximal timestep for an arbitrary choice of the sequence of timesteps and with no further condition on F, and an estimate O(τ2) under some additional conditions. The first result is an improvement over the implicit midpoint method (θ=½), for which an order reduction to O(τ) may occur.
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