In this talk we present the code BiM, based on blended implicit methods [1,2,3], for the numerical solution of stiff initial value problems for ODEs. Such methods are defined in order to meet suitable accuracy and stability requirements and, more importantly, to obtain a discrete problem having a prescribed structure. This, in turn, allows the easy derivation of an efficient nonlinear splitting for its solution. In the case of the methods implemented in the code BiM, such splitting is block diagonal, which makes the extension of the code for parallel computers very straightforward. Numerical tests, comparing the sequential version of the code with the best currently available ones, confirm the potentialities of this approach.

References.

[1] L. Brugnano. Blended Block BVMs (B₃VMs): a Family of Economical Implicit Methods for ODEs, Jour. Comput. Appl. Math. 116 (2000) pp. 41-62.

[2] L. Brugnano, D. Trigiante. Block Implicit Methods for ODEs, in Recent Trends in Numerical Analysis, D. Trigiante Ed., Nova Science Publ. Inc., New York, 2001, pp. 81-105.

[3] L. Brugnano, C. Magherini. Blended Implementation of Block Implicit Methods for ODEs, Appl. Numer. Math. (2002), in press.

Footnotes:

¹ Work supported by C.N.R..

² Joint work with Cecilia MAGHERINI.