Multi-step zero approximations for stepsize control

Applied Numerical Mathematics

Volumn 34, Issue 2, 2000, Pages 167-177

  Butcher, J C ^a   Chan, T M H ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b NATIONAL TAICHUNG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; ESTIMATION; EXTRAPOLATION; POLES AND ZEROS; RUNGE KUTTA METHODS;

EMBEDDED PAIR; MULTI STEP ZERO APPROXIMATIONS; PRINCIPAL LOCAL TRUNCATION ERROR; STEPSIZE CONTROL;

APPROXIMATION THEORY;

EID: 0034230353     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00125-7     Document Type: Article

References (10)

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3. [3] T.M. Chan, Algebraic structure for the analysis of numerical methods, Ph.D. Thesis, The University of Auckland, 1998.
4. [4] J.R. Dormand, P.J. Prince, A family of embedded Runge - Kutta formulae, J. Comput. Appl. Math. 6 (1980) 19-26.
5. [5] E. Fehlberg, Classical fifth-, sixth-, seventh-, and eighth-order Runge - Kutta formulas with stepsize control, NASA Technical Report 287, 1968; extract published in Computing 4 (1969) 93-106.
6. [5] E. Fehlberg, Classical fifth-, sixth-, seventh-, and eighth-order Runge - Kutta formulas with stepsize control, NASA Technical Report 287, 1968; extract published in Computing 4 (1969) 93-106.
7. [6] E. Hairer, G. Wanner, On the Butcher group and general multi-value methods, Computing (Arch. Elektron. Rechnen) 13 (1) (1974) 1-15.
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10. [9] J.H. Verner, Explicit Runge - Kutta methods with estimates of the local truncation error, SIAM J. Numer. Anal. 15 (4) (1978) 772-790.