This PhD thesis consists of a summary and seven papers, where various applications of auto-validated computations are studied.In the first paper we describe a rigorous method to determine unknown parameters in a system of ordinary **differential equations** from measured data with known bounds on the noise of the measurements.Papers II, III, IV, and V are concerned with Abelian integrals. In Paper II, we construct an auto-validated algorithm to compute **Abelian integrals**. In Paper III we investigate, via an example, how one can use this algorithm to determine the possible configurations of limit cycles that can bifurcate from a given Hamiltonian vector field. In Paper IV we construct an example of a perturbation of degree five of a Hamiltonian vector field of degree five, with 27 limit cycles, and in Paper V we construct an example of a perturbation of degree seven of a Hamiltonian vector field of degree seven, with 53 limit cycles. These are new lower bounds for the maximum number of limit cycles that can bifurcate from a Hamiltonian vector field for those degrees.In Papers VI, and VII, we study a certain kind of normal form for real hyperbolic saddles, which is numerically robust…

*Contents*

1 Introduction

1.1 Interval analysis

1.2 Automatic diļ¬erentiation

1.3 Some applications

2 Summary of the papers

2.1 PaperI

2.2 PaperII

2.3 PaperIII

2.4 PaperI

2.5 Paper

2.6 PaperVI

2.7 PaperVII

Summary

Acknowledgement

Bibliography

Author: Johnson, Tomas

Source: Uppsala University Library

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