scholarly journals Local error estimation and step size control in adaptive linear multistep methods

2020 ◽  
Author(s):  
Carmen Arévalo ◽  
Gustaf Söderlind ◽  
Yiannis Hadjimichael ◽  
Imre Fekete
Keyword(s):  
Error Estimation ◽  
Multistep Methods ◽  
Size Control ◽  
Linear Multistep Methods ◽  
Local Error ◽  
Step Size ◽  
Local Error Estimation ◽  
Step Size Control

scholarly journals Embedded Exponentially-Fitted Explicit Runge-Kutta-Nyström Methods for Solving Periodic Problems

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 32
Author(s):  
Musa Demba ◽  
Poom Kumam ◽  
Wiboonsak Watthayu ◽  
Pawicha Phairatchatniyom
Keyword(s):  
Error Estimation ◽  
Variable Step Size ◽  
Local Error ◽  
Step Size ◽  
Local Error Estimation ◽  
Nyström Methods ◽  
Periodic Problems ◽  
Variable Step ◽  
Exponentially Fitted ◽  
Runge Kutta

In this work, a pair of embedded explicit exponentially-fitted Runge–Kutta–Nyström methods is formulated for solving special second-order ordinary differential equations (ODEs) with periodic solutions. A variable step-size technique is used for the derivation of the 5(3) embedded pair, which provides a cheap local error estimation. The numerical results obtained signify that the new adapted method is more efficient and accurate compared with the existing methods.

Co-Simulation: Error Estimation and Macro-Step Size Control

2020 ◽  
Author(s):  
Tobias Meyer ◽  
Jan Kraft ◽  
Bernhard Schweizer
Keyword(s):  
Error Estimation ◽  
Size Control ◽  
Simulation Models ◽  
Error Estimator ◽  
Step Size ◽  
Error Estimators ◽  
Step Size Control ◽  
Communication Time ◽  
Simulation Error ◽  
Time Grid

Abstract Efficiency and accuracy of a co-simulation may considerable be increased by using a variable communication time grid. Therefore, an error estimator for controlling the macro-step size is required. Here, error estimators are derived and investigated for explicit and implicit co-simulation approaches. The manuscript focuses on mechanical co-simulation models. The basic results may, however, also be applied to arbitrary, non-mechanical co-simulation models.

A Step Size Control Method Improving Estimation Speed in Double Talk Term

2013 ◽  
Vol E96.A (7) ◽  
pp. 1543-1551 ◽  
Author(s):  
Takuto YOSHIOKA ◽  
Kana YAMASAKI ◽  
Takuya SAWADA ◽  
Kensaku FUJII ◽  
Mitsuji MUNEYASU ◽  
...  
Keyword(s):  
Control Method ◽  
Size Control ◽  
Step Size ◽  
Step Size Control

Continuation Power Flow: a Parameterization Technique and Adaptive Step Size Control

2021 ◽  
Author(s):  
Alfredo Bonini Neto ◽  
Luis Roberto Almeida Gabriel Filho ◽  
Dilson Amancio Alves
Keyword(s):  
Power Flow ◽  
Size Control ◽  
Step Size ◽  
Adaptive Step Size ◽  
Continuation Power Flow ◽  
Step Size Control ◽  
Adaptive Step

Local error estimation for singly-implicit formulas by two-step Runge-Kutta methods

1992 ◽  
Vol 32 (1) ◽  
pp. 104-117 ◽  
Author(s):  
A. Bellen ◽  
Z. Jackiewicz ◽  
M. Zennaro
Keyword(s):  
Error Estimation ◽  
Local Error ◽  
Local Error Estimation ◽  
Runge Kutta
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