Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0726.65091
Franco, J.M.; Palacios, M.
High-order P-stable multistep methods.
(English)
[J] J. Comput. Appl. Math. 30, No.1, 1-10 (1990). ISSN 0377-0427

A class of two-step methods for solving the initial value problem $y''=f(t,y)$ is presented. The stability polynomial is directly related to the (m,m)-diagonal Padé approximation to the exponential through the $\Sigma$-map, see the reviewer and {\it O. Nevanlinna} [SIAM J. Numer. Anal. 20, 1210-1218 (1983; Zbl 0532.65065)]. Hence the schemes are P- stable, of order 2m and implicit. \par If the implicit equations are solved by a Newton like algorithm at each iteration step the linear system consists of a matrix polynomial in the Jacobian $f\sb y$ of degree m. The powers of the Jacobian $f\sb y$ are avoided by factoring this polynomial. For the linear test equation with an oscillatory forcing term it is shown that the schemes are always in phase in the sense of {\it I. Gladwell}, {\it R. M. Thomas} [Int. J. Numer. Methods Eng. 19, 495-503 (1983; Zbl 0513.65053)]. A numerical comparison with other schemes is presented for linear and nonlinear equations.
[R.Jeltsch (Zürich)]
MSC 2000:
*65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
65L20 Stability of numerical methods for ODE
34A34 Nonlinear ODE and systems, general

Keywords: P-stability; diagonal Padé approximations to the exponential; two-step methods; stability polynomial; numerical comparison

Citations: Zbl 0532.65065; Zbl 0513.65053

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster