On theA-Acceptability of Padé Approximations
- 1 September 1979
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 10 (5) , 1002-1007
- https://doi.org/10.1137/0510091
Abstract
Summary:The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the $A_n$-acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary differential equations as wellKeywords
This publication has 4 references indexed in Scilit:
- C-Polynomials for rational approximation to the exponential functionNumerische Mathematik, 1975
- On the zeros and poles of Padé approximants toe zNumerische Mathematik, 1975
- A-Stable Methods and Padé Approximations to the ExponentialSIAM Journal on Mathematical Analysis, 1973
- Discretization Errors for Well-Set Cauchy Problems. I.Journal of Mathematics and Physics, 1965