Geodesic
Difference schemes for solving the Cauchy problem for a second-order operator differential equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 569-584
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A class of finite-difference schemes for solving an ill-posed Cauchy problem for a second-order linear differential equation with a sectorial operator in a Banach space is studied. Time-uniform estimates of the convergence rate and the error of such schemes are obtained. Previously known estimates are improved due to an optimal choice of initial data for a difference scheme. 
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M. M. Kokurin. Difference schemes for solving the Cauchy problem for a second-order operator differential equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 4, pp. 569-584. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_4_a2/

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