Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Google eBook)

Front Cover
Springer Science & Business Media, Jan 1, 1996 - Mathematics - 614 pages
1 Review
"Whatever regrets may be, we have done our best." (Sir Ernest Shack 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.
  

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Contents

I
1
II
2
III
3
IV
4
V
6
VI
8
VII
11
IX
15
CLXVIII
314
CLXIX
317
CLXX
319
CLXXI
321
CLXXIII
323
CLXXIV
326
CLXXV
328
CLXXVI
329

XI
16
XII
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XIV
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XV
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XVI
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XVII
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XVIII
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XIX
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XXI
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XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXVII
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XXIX
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XXX
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XXXII
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XXXIII
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XXXIV
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XXXV
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XXXVI
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XXXVIII
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XXXIX
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XL
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XLI
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XLII
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XLIII
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XLIV
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XLV
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XLVII
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XLVIII
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XLIX
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L
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LI
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LII
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LIV
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LV
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LVII
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LIX
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LX
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LXI
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LXII
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LXIV
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LXV
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LXVI
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LXVII
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LXVIII
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LXX
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LXXI
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LXXVII
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LXXVIII
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LXXX
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LXXXI
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LXXXIV
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LXXXVII
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LXXXIX
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XC
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XCI
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XCII
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XCV
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XCVI
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XCIX
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C
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CI
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CII
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CIV
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CV
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CVI
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CVII
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CVIII
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CIX
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CX
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CXII
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CXV
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CXVI
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CXVIII
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CXX
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CXXI
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CXXIX
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CXXX
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CXXXI
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CXXXIII
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CXXXIV
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CXXXVIII
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CXL
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CXLI
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CXLIII
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CXLIV
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CXLV
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CXLVI
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CXLVII
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CXLVIII
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CXLIX
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CLI
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CLII
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CLIII
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CLIV
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CLV
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CLVI
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CLVIII
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CLIX
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CLX
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CLXI
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CLXIII
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CLXIV
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CLXV
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CLXVI
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CLXVII
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CLXXVII
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CLXXVIII
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CLXXIX
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CLXXX
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CLXXXII
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CLXXXIII
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CLXXXIV
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CLXXXV
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CLXXXVI
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CLXXXVII
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CLXXXIX
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CXC
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CXCI
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CXCII
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CXCIII
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CXCIV
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CXCV
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CXCVI
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CXCVII
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CXCVIII
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CC
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CCI
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CCII
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CCIII
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CCIV
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CCV
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CCVI
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CCVIII
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CCIX
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CCX
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CCXII
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CCXIII
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CCXIV
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CCXV
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CCXVI
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CCXVII
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CCXVIII
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CCXIX
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CCXX
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CCXXI
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CCXXII
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CCXXIV
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CCXXV
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CCXXVI
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CCXXVII
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CCXXVIII
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CCXXIX
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CCXXX
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CCXXXI
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CCXXXII
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CCXXXIII
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CCXXXIV
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CCXXXVI
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CCXXXVII
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CCXXXVIII
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CCXXXIX
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CCXL
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CCXLI
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CCXLIII
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CCXLIV
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CCXLV
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CCXLVI
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CCXLVII
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CCXLVIII
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CCL
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CCLI
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CCLII
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CCLIII
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CCLIV
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CCLV
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CCLVI
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CCLVIII
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CCLIX
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CCLX
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CCLXI
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CCLXII
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CCLXIII
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CCLXIV
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CCLXV
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CCLXVI
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CCLXVII
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CCLXVIII
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CCLXIX
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CCLXX
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CCLXXI
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CCLXXII
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CCLXXIV
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CCLXXV
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CCLXXVI
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CCLXXVII
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CCLXXVIII
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CCLXXIX
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CCLXXX
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CCLXXXI
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CCLXXXIII
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CCLXXXIV
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CCLXXXV
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CCLXXXVI
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CCLXXXVII
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CCLXXXVIII
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CCLXXXIX
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CCXC
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CCXCI
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CCXCII
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CCXCIII
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CCXCIV
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CCXCV
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CCXCVII
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CCXCVIII
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CCXCIX
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CCC
541
CCCI
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CCCII
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CCCIII
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CCCIV
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CCCV
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CCCVI
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CCCVII
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CCCVIII
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CCCIX
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CCCX
562
CCCXI
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CCCXII
566
CCCXIII
568
CCCXIV
574
CCCXVI
575
CCCXVIII
576
CCCXIX
577
CCCXX
605
CCCXXI
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Common terms and phrases

Popular passages

Page 580 - K. Burrage, A special family of Runge-Kutta methods for solving stiff differential equations, BIT 18 (1978) 22^41.
Page 585 - COPIES AVAILABLE ON REQUEST A selection of papers Simulation of packed-bed separation processes using orthogonal collocation, RK SRIVASTAVA & B JOSEPH. Development and comparison of a generalized semi-implicit Runge-Kutta method with Gear's method for systems of coupled differential and algebraic equations, AN FENG etal.
Page 581 - Semi-implicit Runge-Kutta procedures with error estimates for the numerical integration of stiff systems of ordinary differential equations'.
Page 592 - Generalized Runge-Kutta processes for stable systems with large Lipschitz constants, SIAM J.
Page 584 - Convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints. SIAM J. onNumer. Anal. 30:1467. Johansson, L., 1992, Sliding contact between two elastic half-planes with frictional heat generation and wear, in: "Contact Mechanics," A.Curnier, ed., PPUR, Lausanne.

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About the author (1996)

Ernst Hairer is a Professor of Mathematics at the University of Geneva and has been awarded the Henrici Prize by the Society of Industrial and Applied Mathematics.