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- W2050673367 abstract "For evolution equations with a strongly monotone operator $F(t,u(t))$ we derive unconditional stability and discretization error estimates valid for all $t>0$ . For the $theta$ -method, with $theta = 1-frac{1}{2+ zeta tau^nu }, 0 0$ , we prove an error estimate $O(tau^{frac{4}{3}}), tau rightarrow 0$ , if $nu = frac{1}{3}$ , where $tau$ 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 $F(cdot,cdot)$ , and an optimal estimate $O(tau^2)$ under some additional relation between neighboring steps. The first result is an improvement over the implicit midpoint method $(theta = frac{1}{2})$ , for which an order reduction to $O(tau)$ sometimes may occur for infinitely stiff problems. Numerical tests illustrate the results." @default.
- W2050673367 created "2016-06-24" @default.
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- W2050673367 date "2001-07-01" @default.
- W2050673367 modified "2023-09-27" @default.
- W2050673367 title "Stability and error estimates for the $theta$-method for strongly monotone and infinitely stiff evolution equations" @default.
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- W2050673367 doi "https://doi.org/10.1007/pl00005462" @default.
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