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Numerical Treatment of Inverse Problems in Differential and Integral Equations

Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 — September 3, 1982

  • Peter Deuflhard
  • Ernst Hairer

Part of the Progress in Scientific Computing book series (PSC, volume 2)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Inverse Initial Value Problems in Ordinary Differential Equations

  3. Inverse Boundary and Eigenvalue Problems in Ordinary Differential Equations

    1. Front Matter
      Pages 73-73
    2. P. Deuflhard, G. Bader
      Pages 74-94
    3. Friedrich Franz Seelig, Rainer Füllemann
      Pages 137-145
    4. Ole H. Hald
      Pages 146-149
    5. H. Fiedeldey, R. Lipperheide, S. Sofianos
      Pages 150-160
    6. J. Kautsky, N. K. Nichols, P. van Dooren, L. Fletcher
      Pages 171-178
  4. Inverse Problems in Partial Differential Equations

  5. Fredholm Integral Equations of the First Kind

    1. Front Matter
      Pages 289-289
    2. Stephen W. Provencher, Robert H. Vogel
      Pages 304-319
    3. Johan Philip
      Pages 335-344
    4. Heinz W. Engl
      Pages 345-354
  6. Back Matter
    Pages 355-357

About this book

Introduction

In many scientific or engineering applications, where ordinary differen­ tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas­ ured data and an associated theoretical model, determine unknown para­ meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen­ sitivity coefficients for the model. may be rather time and storage con­ suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev­ itable discretization errors, regularization techniques are necessary.

Keywords

Approximation Eigenvalue Integral equation differential equation numerical methods

Editors and affiliations

  • Peter Deuflhard
    • 1
  • Ernst Hairer
    • 1
  1. 1.Institut für Angewandte Mathematik Abt. Numerische MathematikUniversität HeidelbergHeidelberg 1Fed. Rep. of Germany

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