E. Hairer and G. Wanner, Analysis by Its History, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1996. Home/Search Document Not in Database Summary Related Articles |
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Long-Time Energy Conservation Of Numerical Methods For.. - Ernst Hairer And (1999) (3 citations) Self-citation (Hairer) (Correct)
....central terms involve higher derivatives, we are confronted with singular perturbation problems. We are interested in smooth functions y; z; z k that satisfy the system up to a defect of size O( GammaN ) In the spirit of Euler s derivation of the Euler Maclaurin summation formula (see e.g. [HaW96]) we remove the disturbing higher derivatives by using iteratively the differentiated equations (4.7) 4.9) This leads to a system y 1 = F 1 ( y 1 ; y; z 1 ; z N Gamma1 ; Gamma1 ) z 2 = Gamma1 F 2 ( y 1 ; y; z 1 ; z N Gamma1 ; Gamma1 ) z 1 = ....
E. Hairer and G. Wanner, Analysis by Its History, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1996.
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