Approximate solution of an inhomogeneous abstract differential equation
Applications of Mathematics (2012)
- Volume: 57, Issue: 1, page 31-41
- ISSN: 0862-7940
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topVitásek, Emil. "Approximate solution of an inhomogeneous abstract differential equation." Applications of Mathematics 57.1 (2012): 31-41. <http://eudml.org/doc/246883>.
@article{Vitásek2012,
abstract = {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 $u^\{\prime \}(t)=Au(t)+f(t)$.},
author = {Vitásek, Emil},
journal = {Applications of Mathematics},
keywords = {abstract differential equations; semigroups of operators; rational approximations; A-stability; abstract differential equations; semigroup of operators; rational approximations; -stability},
language = {eng},
number = {1},
pages = {31-41},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximate solution of an inhomogeneous abstract differential equation},
url = {http://eudml.org/doc/246883},
volume = {57},
year = {2012},
}
TY - JOUR
AU - Vitásek, Emil
TI - Approximate solution of an inhomogeneous abstract differential equation
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 31
EP - 41
AB - 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 $u^{\prime }(t)=Au(t)+f(t)$.
LA - eng
KW - abstract differential equations; semigroups of operators; rational approximations; A-stability; abstract differential equations; semigroup of operators; rational approximations; -stability
UR - http://eudml.org/doc/246883
ER -
References
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- Kato, T., Perturbation Theory for Linear Operators, Springer Berlin-Heidelberg-New York (1966). (1966) Zbl0148.12601MR0203473
- Práger, M., Taufer, J., Vitásek, E., Overimplicit multistep methods, Apl. Math. 18 (1973), 399-421. (1973) MR0366041
- Taylor, A. E., Introduction to Functional Analysis, John Wiley & Sons New York (1958). (1958) Zbl0081.10202MR0098966
- Vitásek, E., 10.1007/s10492-007-0008-3, Appl. Math. 52 (2007), 171-183. (2007) Zbl1164.34457MR2305871DOI10.1007/s10492-007-0008-3
- Yosida, K., Functional Analysis, Springer Berlin-Heidelberg-New York (1971). (1971) Zbl0217.16001
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