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Reliable Methods for Computer Simulation

Error Control and Posteriori Estimates

  • 1st Edition, Volume 33 - July 25, 2004
  • Authors: Pekka Neittaanmäki, Sergey R. Repin
  • Language: English
  • Hardback ISBN:
    9 7 8 - 0 - 4 4 4 - 5 1 3 7 6 - 2
  • eBook ISBN:
    9 7 8 - 0 - 0 8 - 0 5 4 0 5 0 - 4

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is… Read more

Reliable Methods for Computer Simulation

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Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.