Local-error estimates for variable-step Runge-Kutta methods

1969 ◽  
pp. 228-233 ◽  
Author(s):  
A. Prothero
Keyword(s):  
Error Estimates ◽  
Local Error ◽  
Variable Step ◽  
Runge Kutta

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.

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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