document: Blended implementation of block implicit methods for ODEs In this paper we further develop a new approach for naturally defining the nonlinear splittings needed for the implementation of block implicit methods for ODEs , which has been considered by Brugnano -LSB- J. Comput . Appl . Math . 116 -LRB- 2000 -RRB- 41 -RSB- and by Brugnano and Trigiante -LSB- in : Recent Trends in Numerical Analysis , Nova Science , New York , 2000 , pp. 81-105 -RSB- . The basic idea is that of defining the numerical method as the combination -LRB- blending -RRB- of two suitable component methods . By carefully choosing such methods , it is shown that very efficient implementations can be obtained . Moreover , some of them , characterized by a diagonal splitting , are well suited for parallel computers . Numerical tests comparing the performances of the proposed implementation with existing ones are also presented , in order to make evident the potential of the approach
doc_bio_tags: B I O B I I O B O O O O O O O O O O O O O B I O O O O O B I I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: nonlinear splittings block implicit methods blended implementation odes numerical method diagonal splitting parallel computers numerical tests