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A Convergence Analy...
A Convergence Analysis of the Peaceman-Rachford Scheme for Semilinear Evolution Equations
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- Hansen, Eskil (författare)
- Lund University,Lunds universitet,Numerisk analys,Forskargrupper vid Lunds universitet,Partiella differentialekvationer,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Numerical Analysis,Lund University Research Groups,Partial differential equations,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Henningsson, Erik (författare)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- Society for Industrial & Applied Mathematics (SIAM), 2013
- 2013
- Engelska 11 s.
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 51:4, s. 1900-1910
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Abstract
Ämnesord
Stäng
- The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman--Rachford scheme in the setting of dissipative evolution equations on Hilbert spaces. We do not assume Lipschitz continuity of the nonlinearity, as previously done in the literature. First or second order convergence is derived, depending on the regularity of the solution, and a shortened proof for $o(1)$-convergence is given when only a mild solution exits. The analysis is also extended to the Lie scheme in a Banach space framework. The convergence results are illustrated by numerical experiments for Caginalp's solidification model and the Gray--Scott pattern formation problem.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Peaceman--Rachford scheme
- convergence order
- semilinear evolution equations
- reaction-diusion systems
- dissipative operators
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- art (ämneskategori)
- ref (ämneskategori)
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