ABSTRACT. In a previous paper [3], some numerical methods for stochastic ordinary differential equations (SODEs), based on Linear Multistep Formulae (LMF), were proposed. Nevertheless, a formal proof for the convergence of such methods is still lacking. We here provide such a proof, based on a matrix formulation of the discrete problem, which allows some more insight in the structure of LMF-type methods for SODEs.
On the convergence of LMF-type methods for SODEs / L. Brugnano; G. Carreras; K. Burrage. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5454. - STAMPA. - 1:(2004), pp. 297-313. [10.1007/s00009-004-0017-3]
On the convergence of LMF-type methods for SODEs
BRUGNANO, LUIGI;
2004
Abstract
ABSTRACT. In a previous paper [3], some numerical methods for stochastic ordinary differential equations (SODEs), based on Linear Multistep Formulae (LMF), were proposed. Nevertheless, a formal proof for the convergence of such methods is still lacking. We here provide such a proof, based on a matrix formulation of the discrete problem, which allows some more insight in the structure of LMF-type methods for SODEs.File | Dimensione | Formato | |
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