Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type - Part II: Linear multistep methods

K. Nipp; D. Stoffer

doi:10.1007/s002110050218

Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type - Part II: Linear multistep methods

Numerische Mathematik ◽

10.1007/s002110050218 ◽

1996 ◽

Vol 74 (3) ◽

pp. 305-323 ◽

Cited By ~ 7

Author(s):

K. Nipp ◽

D. Stoffer

Keyword(s):

Singular Perturbation ◽

Numerical Integration ◽

Error Estimates ◽

Invariant Manifolds ◽

Multistep Methods ◽

Global Error ◽

Linear Multistep Methods ◽

Stiff Systems ◽

Integration Schemes ◽

Global Error Estimates

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Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type -- Part I: RK-methods

Numerische Mathematik ◽

10.1007/s002110050118 ◽

1995 ◽

Vol 70 (2) ◽

pp. 245-257 ◽

Cited By ~ 13

Author(s):

K. Nipp ◽

D. Stoffer

Keyword(s):

Singular Perturbation ◽

Numerical Integration ◽

Error Estimates ◽

Invariant Manifolds ◽

Global Error ◽

Stiff Systems ◽

Integration Schemes ◽

Global Error Estimates

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Global Error Estimates for ODEs Based on Extrapolation Methods

SIAM Journal on Scientific and Statistical Computing ◽

10.1137/0906001 ◽

1985 ◽

Vol 6 (1) ◽

pp. 1-14 ◽

Cited By ~ 13

Author(s):

L. F. Shampine ◽

L. S. Baca

Keyword(s):

Error Estimates ◽

Global Error ◽

Extrapolation Methods ◽

Global Error Estimates

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Exponentially-fitted and trigonometrically-fitted symmetric linear multistep methods for the numerical integration of orbital problems

Physics Letters A ◽

10.1016/s0375-9601(03)01109-5 ◽

2003 ◽

Vol 315 (6) ◽

pp. 437-446 ◽

Cited By ~ 10

Author(s):

T.E. Simos

Keyword(s):

Numerical Integration ◽

Multistep Methods ◽

Linear Multistep Methods ◽

Orbital Problems ◽

Exponentially Fitted

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Towards a regularity theory for ReLU networks – chain rule and global error estimates

2019 13th International conference on Sampling Theory and Applications (SampTA) ◽

10.1109/sampta45681.2019.9031005 ◽

2019 ◽

Author(s):

Julius Berner ◽

Dennis Elbrachter ◽

Philipp Grohs ◽

Arnulf Jentzen

Keyword(s):

Error Estimates ◽

Regularity Theory ◽

Chain Rule ◽

Global Error ◽

Global Error Estimates

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The efficiency of second derivative multistep methods for the numerical integration of stiff systems

Journal of the Nigerian Mathematical Society ◽

10.1016/j.jnnms.2016.02.002 ◽

2016 ◽

Vol 35 (1) ◽

pp. 107-127 ◽

Cited By ~ 2

Author(s):

D.G. Yakubu ◽

S. Markus

Keyword(s):

Numerical Integration ◽

Multistep Methods ◽

Second Derivative ◽

Stiff Systems

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Convergence of linear multistep methods for two-parameter singular perturbation problems

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/bf02669574 ◽

2001 ◽

Vol 17 (2) ◽

pp. 207-217 ◽

Cited By ~ 1

Author(s):

Xiao Aiguo ◽

Li Shoufu ◽

Fu Hongyuan ◽

Chen Guangnan

Keyword(s):

Singular Perturbation ◽

Multistep Methods ◽

Singular Perturbation Problems ◽

Linear Multistep Methods ◽

Perturbation Problems ◽

Two Parameter

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Errors of linear multistep methods and Runge-Kutta methods for singular perturbation problems with delays

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(02)00223-7 ◽

2002 ◽

Vol 44 (8-9) ◽

pp. 1157-1173 ◽

Cited By ~ 1

Author(s):

Siqing Gan ◽

Geng Sun ◽

Weimin Zheng

Keyword(s):

Singular Perturbation ◽

Multistep Methods ◽

Singular Perturbation Problems ◽

Linear Multistep Methods ◽

Runge Kutta ◽

Perturbation Problems

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Second derivative continuous linear multistep methods for the numerical integration of Stiff system of ordinary differential equations.

Journal of the Nigerian Association of Mathematical Physics ◽

10.4314/jonamp.v11i1.40210 ◽

2008 ◽

Vol 11 (1) ◽

Author(s):

F O Otunta ◽

MN Ikhile ◽

RI Okuonghae

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Numerical Integration ◽

Multistep Methods ◽

Linear Multistep Methods ◽

Second Derivative ◽

Continuous Linear ◽

Stiff System

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Blended extended linear multistep methods for the accurate numerical integration of stiff initial value problems

Applied Numerical Mathematics ◽

10.1016/0168-9274(85)90016-9 ◽

1985 ◽

Vol 1 (3) ◽

pp. 195-216 ◽

Cited By ~ 1

Author(s):

J.R. Cash ◽

N. Lambrou

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Multistep Methods ◽

Linear Multistep Methods ◽

Initial Value ◽

Stiff Initial Value Problems

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On the numerical integration of nonlinear initial value problems by linear multistep methods

BIT Numerical Mathematics ◽

10.1007/bf01932399 ◽

1977 ◽

Vol 17 (1) ◽

pp. 58-71 ◽

Cited By ~ 28

Author(s):

Olavi Nevanlinna

Keyword(s):

Numerical Integration ◽

Initial Value Problems ◽

Multistep Methods ◽

Linear Multistep Methods ◽

Initial Value

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