Order conditions of Runge-Kutta methods for index 2 systems

Lecture Notes in Mathematics - The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods ◽

10.1007/bfb0093952 ◽

1989 ◽

pp. 55-70 ◽

Author(s):

Ernst Hairer ◽

Michel Roche ◽

Christian Lubich

Keyword(s):

Order Conditions ◽

Index 2 ◽

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Order Conditions for Index 2 DAE

Springer Series in Computational Mathematics - Solving Ordinary Differential Equations II ◽

10.1007/978-3-642-05221-7_35 ◽

1996 ◽

pp. 506-518

Author(s):

Ernst Hairer ◽

Gerhard Wanner

Keyword(s):

Order Conditions ◽

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An alternative approach for order conditions of Runge-Kutta-Nyström methods

Advances in Computational Mathematics ◽

10.1007/s10444-021-09894-3 ◽

2021 ◽

Vol 47 (5) ◽

Author(s):

Xue Sun ◽

Zhongli Liu ◽

Hongjiong Tian

Keyword(s):

Order Conditions ◽

Nyström Methods ◽

Alternative Approach ◽

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Order Conditions of Stochastic Runge--Kutta Methods by B-Series

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142999363206 ◽

2000 ◽

Vol 38 (5) ◽

pp. 1626-1646 ◽

Author(s):

K. Burrage ◽

P. M. Burrage

Keyword(s):

Order Conditions ◽

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Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations

Stochastic Analysis and Applications ◽

10.1080/07362990500397699 ◽

2006 ◽

Vol 24 (1) ◽

pp. 97-134 ◽

Author(s):

Andreas Rößler

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Rooted Tree ◽

Order Conditions ◽

Weak Approximation ◽

Tree Analysis ◽

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On simplifying assumptions of Runge-Kutta methods for index 2 differential algebraic problems

Computing ◽

10.1007/bf02238131 ◽

1995 ◽

Vol 54 (2) ◽

pp. 185-190 ◽

Author(s):

I. Higueras

Keyword(s):

Simplifying Assumptions ◽

Index 2 ◽

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Enumeration results for Runge–Kutta methods for index 2 DAEs

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2006.12.018 ◽

2008 ◽

Vol 213 (1) ◽

pp. 294-299

Author(s):

Frank Cameron

Keyword(s):

Index 2 ◽

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Half-Explicit Runge–Kutta Methods for Differential-Algebraic Systems of Index 2

SIAM Journal on Numerical Analysis ◽

10.1137/0730025 ◽

1993 ◽

Vol 30 (2) ◽

pp. 538-552 ◽

Author(s):

V. Brasey ◽

E. Hairer

Keyword(s):

Algebraic Systems ◽

Index 2 ◽

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On order conditions for modified Patankar–Runge–Kutta schemes

Applied Numerical Mathematics ◽

10.1016/j.apnum.2017.09.004 ◽

2018 ◽

Vol 123 ◽

pp. 159-179 ◽

Author(s):

S. Kopecz ◽

A. Meister

Keyword(s):

Order Conditions ◽

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Reversible methods of Runge-Kutta type for Index-2 DAEs

Numerische Mathematik ◽

10.1007/s00211-003-0499-0 ◽

2004 ◽

Vol 97 (3) ◽

pp. 427-440

Author(s):

R.P.K. Chan ◽

P. Chartier ◽

A. Murua

Keyword(s):

Index 2 ◽

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Behavior of Runge–Kutta discretizations near equilibria of index 2 differential algebraic systems

Applied Numerical Mathematics ◽

10.1016/s0168-9274(01)00165-9 ◽

2002 ◽

Vol 42 (1-3) ◽

pp. 425-435

Author(s):

Johannes Schropp

Keyword(s):

Algebraic Systems ◽

Index 2 ◽

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