Numerical analysis view on the general Trotter-Kato product formulae
We show that the abstract operator-theoretic (general) Trotter–Kato formulae yield the convergence of numerical methods used for solving differential equations. These methods combine operator splitting procedures with certain time discretisation schemes which should be consistent, strongly Astable,...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-140-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/73931 |
| Tartalmi kivonat: | We show that the abstract operator-theoretic (general) Trotter–Kato formulae yield the convergence of numerical methods used for solving differential equations. These methods combine operator splitting procedures with certain time discretisation schemes which should be consistent, strongly Astable, positive rational approximations of the exponential function. We also show that it is possible to apply more numerical steps in one splitting time step and the convergence results remain true. |
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| Terjedelem/Fizikai jellemzők: | 307-329 |
| ISSN: | 2064-8316 |