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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics Book 31)

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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics Book 31)

4.85 12,176 ratings · 4,960 reviews
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Published January 1, 2006
ISBN 35686752
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Ernst Hairer
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Ernst Hairer is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Ernst Hairer enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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George Anderson
George Anderson January 19, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Ryan  Davis
Ryan Davis October 08, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Robert Smith
Robert Smith April 12, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Margaret Nelson
Margaret Nelson September 09, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Donna Rivera July 04, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
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Nicholas Young January 18, 2024
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Deborah Lewis May 12, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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James Collins May 29, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Robert Flores
Robert Flores October 12, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Betty Gomez
Betty Gomez December 24, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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Margaret Rivera June 12, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars.
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Margaret Martin October 08, 2024
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
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A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
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Donna Clark May 07, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Jennifer Wilson November 26, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Jessica Martin
Jessica Martin August 19, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Kevin Robinson July 12, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Melissa Harris September 01, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Betty Clark October 16, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Daniel Jones September 07, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Margaret Robinson
Margaret Robinson October 01, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Anthony Turner
Anthony Turner February 03, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Eric Reyes
Eric Reyes November 03, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Laura Scott
Laura Scott June 11, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Lisa Scott
Lisa Scott August 24, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Cynthia Flores
Cynthia Flores July 19, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Joseph Smith
Joseph Smith August 25, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Melissa Miller
Melissa Miller February 05, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Jessica Thomas
Jessica Thomas March 22, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Matthew Lee
Matthew Lee November 07, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Sandra Campbell
Sandra Campbell December 05, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Jennifer Hill
Jennifer Hill May 30, 2024
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Mark Green
Mark Green March 13, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Jacob Lewis
Jacob Lewis October 19, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Steven Thomas
Steven Thomas June 09, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Daniel Jones
Daniel Jones July 27, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Nicholas Jackson
Nicholas Jackson July 26, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Rebecca Gonzalez
Rebecca Gonzalez January 27, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Jessica Thomas
Jessica Thomas April 17, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Mary Wilson
Mary Wilson August 28, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Sarah Cruz
Sarah Cruz May 29, 2024
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Jacob Roberts
Jacob Roberts January 01, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Charles Taylor
Charles Taylor March 05, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Gary Jackson
Gary Jackson May 19, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Joshua Cruz
Joshua Cruz November 30, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Laura Miller
Laura Miller February 06, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Edward Collins
Edward Collins November 04, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Deborah Smith
Deborah Smith September 29, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Cynthia Turner
Cynthia Turner February 28, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Ryan Gomez
Ryan Gomez June 01, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Carol Lee
Carol Lee May 14, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Cynthia Ramirez
Cynthia Ramirez October 17, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Amanda King
Amanda King February 09, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Laura Scott
Laura Scott March 30, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Kimberly Thomas
Kimberly Thomas October 18, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Ryan  Davis
Ryan Davis October 06, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Dorothy Baker
Dorothy Baker January 25, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Kimberly Roberts
Kimberly Roberts May 06, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Amanda King
Amanda King July 20, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
David Flores
David Flores June 08, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Kimberly Brown
Kimberly Brown December 29, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Steven Sanchez
Steven Sanchez September 15, 2025
I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Lisa Nelson
Lisa Nelson September 17, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Michael White
Michael White June 28, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Sandra Allen
Sandra Allen January 28, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Gary Turner
Gary Turner June 13, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Ryan Garcia
Ryan Garcia June 06, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
George Nguyen
George Nguyen August 08, 2025
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
Donald Hall
Donald Hall February 12, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Sharon Collins
Sharon Collins April 09, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Margaret Nelson
Margaret Nelson December 26, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Donald Thomas
Donald Thomas April 05, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Margaret White
Margaret White March 30, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Sandra Flores
Sandra Flores October 14, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Anthony Turner
Anthony Turner March 10, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Daniel Gonzalez
Daniel Gonzalez July 16, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Margaret White
Margaret White May 11, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Donna Roberts
Donna Roberts November 24, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Robert Flores
Robert Flores December 21, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Robert Martin
Robert Martin August 28, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Michael Lopez
Michael Lopez April 15, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
George Nguyen
George Nguyen January 26, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Matthew Scott
Matthew Scott December 31, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Anthony Diaz
Anthony Diaz December 09, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
John Collins
John Collins May 15, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Karen Johnson
Karen Johnson August 13, 2024
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Lisa Williams
Lisa Williams July 10, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Amanda Garcia
Amanda Garcia August 20, 2024
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Emily Allen
Emily Allen January 11, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Rebecca Lopez
Rebecca Lopez May 07, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Elizabeth Mitchell
Elizabeth Mitchell June 19, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
George Edwards
George Edwards July 09, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Edward Martin
Edward Martin August 31, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Stephanie  Davis
Stephanie Davis December 05, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Michael Gonzalez
Michael Gonzalez January 15, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Thomas Perez
Thomas Perez July 06, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Jacob Lee
Jacob Lee April 29, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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