Numerical Treatment of Inverse Problems in Differential and Integral Equations

1. Front Matter

   Pages i-xiii

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2. Inverse Initial Value Problems in Ordinary Differential Equations

   1. Front Matter

      Pages 1-1

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   2. Smooth Numerical Solutions of Ordinary Differential Equations

      • C. W. Gear, Thu Vu

      Pages 2-12

   3. Towards Parameter Identification for Large Chemical Reaction Systems

      • U. Nowak, P. Deuflhard

      Pages 13-26

   4. Identification of Rate Constants in Bistable Chemical Reactions

      • Johannes Schlöder, Hans Georg Bock

      Pages 27-47

   5. New Methods of Parameter Identification in Kinetics of Closed and Open Reaction Systems

      • H. Lachmann

      Pages 48-61

   6. On the Estimation of Small Perturbations in Ordinary Differential Equations

      • Pedro E. Zadunaisky

      Pages 62-72

3. Inverse Boundary and Eigenvalue Problems in Ordinary Differential Equations

   1. Front Matter

      Pages 73-73

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   2. Multiple Shooting Techniques Revisited

      • P. Deuflhard, G. Bader

      Pages 74-94

   3. Recent Advances in Parameteridentification Techniques for O.D.E.

      • H. G. Bock

      Pages 95-121

   4. Some Examples of Parameter Estimation by Multiple Shooting

      • Roland England

      Pages 122-136

   5. Unrestricted Harmonic Balance III, Application to Running and Standing Chemical Waves

      • Friedrich Franz Seelig, Rainer Füllemann

      Pages 137-145

   6. Inverse Eigenvalue Problems for the Mantle

      • Ole H. Hald

      Pages 146-149

   7. Inverse Problem of Quantal Potential Scattering at Fixed Energy

      • H. Fiedeldey, R. Lipperheide, S. Sofianos

      Pages 150-160

   8. An Inverse Eigenvalue Problem from Control Theory

      • L. R. Fletcher

      Pages 161-170

   9. Numerical Methods for Robust Eigenstructure Assignment in Control System Design

      • J. Kautsky, N. K. Nichols, P. van Dooren, L. Fletcher

      Pages 171-178

4. Inverse Problems in Partial Differential Equations

   1. Front Matter

      Pages 179-179

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   2. Some Inverse Problems in Electrocardiology

      • Piero Colli Franzone

      Pages 180-205

   3. Determination of Coefficients in Reservoir Simulation

      • Richard E. Ewing

      Pages 206-226

   4. Identification of Nonlinear Soil Physical Parameters from an Input-Output Experiment

      • Ulrich Hornung

      Pages 227-237

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.

• Approximation
• Eigenvalue
• Integral equation
• differential equation
• numerical methods

• Institut für Angewandte Mathematik Abt. Numerische Mathematik, Universität Heidelberg, Heidelberg 1, Fed. Rep. of Germany

  Peter Deuflhard, Ernst Hairer

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