The present paper is devoted to study the first order of accuracy absolute stable difference scheme for the approximate solution of the space identification problem for the elliptic‐telegraph equation in Hilbert spaces with the self‐adjoint positive definite operator. The main theorem on the stability of the difference scheme is established. In applications, theorems on the stability of difference schemes for two types of the space identification problems for multidimensional elliptic‐telegraph partial differential equations are proved. Numerical analysis is provided.

中文翻译：

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椭圆电报方程的时空相关源识别问题的绝对稳定差分格式

本文致力于研究具有自伴正定算子的希尔伯特空间中的椭圆电报方程空间识别问题的近似解的一阶精度绝对稳定差分方案。建立了差分格式稳定性的主要定理。在实际应用中，证明了多维椭圆电报偏微分方程两类空间识别问题差分格式稳定性的定理。提供数值分析。