Summary
This paper is to show, if the abstract Cauchy problem has a stable difference scheme, then the Cauchy problem of a perturbed equation has also a stable difference scheme when a perturbing operator and its difference approximation have some suitable properties. And it will be noted this result is applicable to parabolic differential equations and their lower order terms, when parabolic difference schemes are used as original difference schemes.
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Sunouchi, H. Perturbation theory of difference schemes. Numer. Math. 12, 454–458 (1968). https://doi.org/10.1007/BF02161369
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DOI: https://doi.org/10.1007/BF02161369