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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Published in:Journal of computational and applied mathematics Vol. 189; no. 1; pp. 34 - 50
Main Authors: Brugnano, Luigi, Magherini, Cecilia, Mugnai, Filippo
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.05.2006
Elsevier
Subjects:
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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Summary: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.
Bibliography:SourceType-Scholarly Journals-2
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.05.005