Blended implicit methods for the numerical solution of DAE problems

Recently, a new approach for solving the discrete problems, generated by the application of block implicit methods for the numerical solution of initial value problems for ODEs, has been devised [L. Brugnano, Blended block BVMs (B 3 VMs): a family of economical implicit methods for ODEs, J. Comput....

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Vydané v:	Journal of computational and applied mathematics Ročník 189; číslo 1; s. 34 - 50
Hlavní autori:	Brugnano, Luigi, Magherini, Cecilia, Mugnai, Filippo
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.05.2006 Elsevier
Predmet:	Blended implicit methods Differential algebraic equations Exact sciences and technology Iterative solution of algebraic systems Mathematics Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical methods for DAEs Numerical methods for ODEs Ordinary differential equations Sciences and techniques of general use Stiff problems 65L05 65L06 Stiff problems Differential algebraic equations Numerical methods for ODEs 65L80 Blended implicit methods Ordinary differential equations Numerical methods for DAEs 65H10 Iterative solution of algebraic systems Differential equation Stiff problem Initial value problem Iterative method Numerical method Partial differential equation Numerical analysis 65H10 Ordinary differential equations Applied mathematics Numerical solution Algebraic equation
ISSN:	0377-0427, 1879-1778
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Popis
Shrnutí:	Recently, a new approach for solving the discrete problems, generated by the application of block implicit methods for the numerical solution of initial value problems for ODEs, has been devised [L. Brugnano, Blended block BVMs (B 3 VMs): a family of economical implicit methods for ODEs, J. Comput. Appl. Math. 116 (2000) 41–62; L. Brugnano, C. Magherini, Blended implementation of block implicit methods for ODEs, Appl. Numer. Math. 42 (2002) 29–45; L. Brugnano, D. Trigiante, Block implicit methods for ODEs, in: D. Trigiante (Ed.), Recent Trends in Numerical Analysis, Nova Science Publishers, New York, 2001, pp. 81–105]. This approach is based on the so-called blended implementation of the methods, giving corresponding blended implicit methods. The latter have been implemented in the computational code BiM [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164–165 (2004) 145–158]. Blended implicit methods are here extended to handle the numerical solution of DAE problems, resulting in a straightforward generalization of the basic approach.
Bibliografia:	SourceType-Scholarly Journals-2 ObjectType-Feature-2 ObjectType-Conference Paper-1 content type line 23 SourceType-Conference Papers & Proceedings-1 ObjectType-Article-3
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2005.05.005