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Stability and convergence of second order backward differentiation schemes for parabolic Hamilton–Jacobi–Bellman equations

Abstract:

We study a second order Backward Differentiation Formula (BDF) scheme for the numerical approximation of linear parabolic equations and nonlinear Hamilton–Jacobi–Bellman (HJB) equations. The lack of monotonicity of the BDF scheme prevents the use of well-known convergence results for solutions in the viscosity sense. We first consider one-dimensional uniformly parabolic equations and prove stability with respect to perturbations, in the L2 norm for linear and semi-linear equations, and in the...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00211-021-01202-x

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer
Journal:
Numerische Mathematik More from this journal
Volume:
148
Issue:
1
Pages:
187–222
Publication date:
2021-05-20
Acceptance date:
2021-04-16
DOI:
EISSN:
0945-3245
ISSN:
0029-599X
Language:
English
Keywords:
Pubs id:
1172715
Local pid:
pubs:1172715
Deposit date:
2021-04-21

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