Local error estimates for moderately smooth problems: Part I – ODEs and DAEs | Zendy

Thorsten Sickenberger | Zendy; Ewa Weinmüller | Zendy; Renate Winkler | Zendy

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Local error estimates for moderately smooth problems: Part I – ODEs and DAEs

Author(s) -

Thorsten Sickenberger,

Ewa Weinmüller,

Renate Winkler

Publication year - 2006

Publication title -

bit numerical mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.904

H-Index - 59

eISSN - 1572-9125

pISSN - 0006-3835

DOI - 10.1007/s10543-006-0097-5

Subject(s) - ode , ordinary differential equation , mathematics , context (archaeology) , differential algebraic equation , initial value problem , noise (video) , differential equation , computer science , mathematical optimization , mathematical analysis , paleontology , artificial intelligence , image (mathematics) , biology

The paper consists of two parts. In the first part, we propose a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary dif- ferential equations (ODEs) and index 1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we develop local error estimates for the case when the problem data is only moderately smooth. Numerical experiments illustrate the performance of the mesh adaptation based on the error estimation developed in this paper. In the second part of the paper, we will consider the estimation of local errors in context of stochastic differential equations with small noise. AMS subject classification (2000): 65L06, 65L80, 65L50, 65L05.

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