Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs

L. Even-Dar Mandel; S. Schochet

doi:10.1051/m2an/2016029

Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs

L. Even-Dar Mandel, S. Schochet

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Solutions of certain finite-difference schemes for singularly-perturbed evolutionary PDEs converge as the perturbation parameter and/or the discretization parameters tend to zero. Under suitable hypotheses a sharp convergence rate of order one-half in the time step, uniform in the perturbation parameter, is obtained.

Original language	English
Pages (from-to)	587-614
Number of pages	28
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	51
Issue number	2
DOIs	https://doi.org/10.1051/m2an/2016029
State	Published - 1 Mar 2017

Keywords

Discrete Sobolev spaces
Rate of convergence
Singular limits

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abstract = "Solutions of certain finite-difference schemes for singularly-perturbed evolutionary PDEs converge as the perturbation parameter and/or the discretization parameters tend to zero. Under suitable hypotheses a sharp convergence rate of order one-half in the time step, uniform in the perturbation parameter, is obtained.",

keywords = "Discrete Sobolev spaces, Rate of convergence, Singular limits",

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Convergence of solutions to finite difference schemes for singular limits of nonlinear evolutionary PDEs

Abstract

Keywords

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