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Asymptotic factorization of evolution equations which involve linear operators
Author(s) -
Cooke Charlie H.,
McMorran Andrew G.
Publication year - 1991
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690070205
Subject(s) - mathematics , factorization , operator (biology) , linear operators , order (exchange) , work (physics) , mathematical analysis , algorithm , chemistry , quantum mechanics , physics , biochemistry , finance , repressor , transcription factor , economics , bounded function , gene
Operator splitting for evolution equations which involve linear operators is investigated. A systematic method for identifying multifactor fractional‐step operator splittings is proposed. The classical second‐order accurate splittings of Strang readily emerge, as well as various third‐order splittings of nonstandard type. Factorizations possessing mixed positive‐negative fractional steps are discovered, as well as bizarre splittings whose factors include complex fractional steps. It is found that no higher‐order accurate splitting which employs all positive fractional steps and which possesses less than nine operator factors can exist. For the linear case this implies second‐order accurate splittings are optimal, as a further increase of one power in accuracy essentially requires a three‐fold increase in work. This estimate slightly improves, for cases where the nonstandard splittings can be employed. Some numerical experiments which illustrate the theory are provided.