Abstract
In the present chapter we consider the well-posedness of an abstract boundary-value problem for differential equations of elliptic type
in an arbitrary Banach spaceEwith the positive operator A. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition on three points for the numerical solutions of this problem are presented. The well-posedness of these difference schemes in various Banach spaces are studied. The stability and coercive stability estimates in Holder norms for solutions of the high order of accuracy difference schemes of the mixed type boundary-value problems for elliptic equations are obtained.
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© 2004 Springer Basel AG
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Ashyralyev, A., Sobolevskii, P.E. (2004). Partial Differential Equations of Elliptic Type. In: New Difference Schemes for Partial Differential Equations. Operator Theory: Advances and Applications, vol 148. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7922-4_5
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DOI: https://doi.org/10.1007/978-3-0348-7922-4_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9622-1
Online ISBN: 978-3-0348-7922-4
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