Finite difference semidiscretization methods for solving an ill-posed Cauchy problem in a Hilbert space are investigated. The problems involve linear positively definite selfadjoint operators. We justify an a posteriori scheme for the choice of the time-discretization step and establish accuracy estimates in terms of the error level of input data.

中文翻译：

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希尔伯特空间中不适定柯西问题的有限差分方法中时间离散步骤的后验选择

研究了求解希尔伯特空间中不适定柯西问题的有限差分半离散化方法。这些问题涉及线性正定自伴算子。我们为选择时间离散步骤证明了一种后验方案，并根据输入数据的误差水平建立了准确度估计。