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- Steinebach G. Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks
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- Steinebach G. Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks
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within the Julia Differential Equations package.
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In: BIT Numerical Mathematics, 63(2), 2023
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""",
@@ -1056,7 +1056,7 @@ lower if not corrected).
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""",
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"Rodas4P",
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references ="""
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- Steinebach G., Rodas23W / Rodas32P - a Rosenbrock-type method for DAEs with additional error estimate
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- Steinebach G., Rodas23W / Rodas32P - a Rosenbrock-type method for DAEs with additional error estimate
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for dense output and Julia implementation,
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In progress.
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""",
@@ -1070,7 +1070,7 @@ of Roadas4P and in case of inexact Jacobians a second order W method.
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""",
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"Rodas4P2",
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references ="""
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- Steinebach G., Rodas23W / Rodas32P - a Rosenbrock-type method for DAEs with additional error estimate
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- Steinebach G., Rodas23W / Rodas32P - a Rosenbrock-type method for DAEs with additional error estimate
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for dense output and Julia implementation,
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In progress.
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""",
@@ -1095,7 +1095,7 @@ Has improved stability in the adaptive time stepping embedding.
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""",
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"Rodas5P",
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references ="""
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- Steinebach G. Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks
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- Steinebach G. Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks
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within the Julia Differential Equations package.
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In: BIT Numerical Mathematics, 63(2), 2023
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""",
@@ -1225,10 +1225,10 @@ references = """
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ROS2PRTableau()
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2nd order stiffly accurate Rosenbrock method with 3 internal stages with (Rinf=0).
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For problems with medium stiffness the convergence behaviour is very poor and it is recommended to use
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For problems with medium stiffness the convergence behaviour is very poor and it is recommended to use
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[`ROS2S`](@ref) instead.
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionROS2PRTableau() # 2nd order
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@docrosenbrock_docstring(
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"""
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2nd order stiffly accurate Rosenbrock method with 3 internal stages with (Rinf=0).
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For problems with medium stiffness the convergence behaviour is very poor and it is recommended to use
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For problems with medium stiffness the convergence behaviour is very poor and it is recommended to use
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[`ROS2S`](@ref) instead.
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""",
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"ROS2PR",
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2nd order stiffly accurate Rosenbrock-Wanner W-method with 3 internal stages with B_PR consistent of order 2 with (Rinf=0).
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More Information at https://doi.org/10.24355/dbbs.084-201408121139-0
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionROS2STableau() # 2nd order
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3nd order stiffly accurate Rosenbrock-Wanner method with 3 internal stages with B_PR consistent of order 3, which is strongly A-stable with Rinf~=-0.73.
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionROS3PRTableau() # 3rd order
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3nd order stiffly accurate Rosenbrock method with 3 internal stages with B_PR consistent of order 3, which is strongly A-stable with Rinf~=-0.73
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Convergence with order 4 for the stiff case, but has a poor accuracy.
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionScholz4_7Tableau() # 3rd order
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B_PR consistent of order 2 with Rinf=0.
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The order of convergence decreases if medium stiff problems are considered, but it has good results for very stiff cases.
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionROS3PRLTableau() # 3rd order
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B_PR consistent of order 3.
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The order of convergence does NOT decreases if medium stiff problems are considered as it does for [`ROS3PRL`](@ref).
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Rang, Joachim (2014): The Prothero and Robinson example:
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Rang, Joachim (2014): The Prothero and Robinson example:
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Convergence studies for Runge-Kutta and Rosenbrock-Wanner methods. https://doi.org/10.24355/dbbs.084-201408121139-0
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"""
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functionROS3PRL2Tableau() # 3rd order
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4rd order L-stable Rosenbrock-Krylov method with 4 internal stages,
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with a 3rd order embedded method which is strongly A-stable with Rinf~=0.55. (when using exact Jacobians)
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Tranquilli, Paul and Sandu, Adrian (2014): Rosenbrock--Krylov Methods for Large Systems of Differential Equations
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Tranquilli, Paul and Sandu, Adrian (2014): Rosenbrock--Krylov Methods for Large Systems of Differential Equations
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https://doi.org/10.1137/130923336
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"""
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functionROK4aTableau() # 4rd order
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""",
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"ROK4a",
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references ="""
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- Tranquilli, Paul and Sandu, Adrian (2014):
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- Tranquilli, Paul and Sandu, Adrian (2014):
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Rosenbrock--Krylov Methods for Large Systems of Differential Equations
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