Geodesic
Approximate solution of an inhomogeneous abstract differential equation
Applications of Mathematics, Tome 57 (2012) no. 1, pp. 31-41.

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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 $u'(t)=Au(t)+f(t)$.
DOI : 10.1007/s10492-012-0003-1
Classification : 34A45, 34G10, 34K30, 35K90, 41A20, 47D03
Keywords: abstract differential equations; semigroups of operators; rational approximations; A-stability 
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Vitásek, Emil. Approximate solution of an inhomogeneous abstract differential equation. Applications of Mathematics, Tome 57 (2012) no. 1, pp. 31-41. doi : 10.1007/s10492-012-0003-1. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0003-1/

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