Construction of unconditionally stable difference schemes based on stability of perturbed difference scheme

2019

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DOI 10.1063/1.5136188
Data confidence 70 medium
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Abstract

In this paper, unconditionally stable difference schemes are constructed to solve the ill-posed Cauchy problem associated with a one-dimensional coefficient inverse problem. The construction of an unconditionally stable scheme is based on the stability of a three-layer perturbed difference scheme with two weights. The research method is based on obtaining discrete analogs of a priori weight estimates of the Carleman type.