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abstract differential equations; semigroups of operators; rational approximations; A-stability
Recently, we have developed the necessary and sufficient conditions under which a rational function $F(hA)$ approximates the semigroup of operators $\exp (tA)$ generated by an infinitesimal operator $A$. The present paper extends these results to an inhomogeneous equation $u'(t)=Au(t)+f(t)$.
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