In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these two fields in abstract terms. Then we expand on this initial concept, using it to devise visualisation methods and a wide variety of solvers for flutter problems. We assess these solvers, applying them to real-life aeroelastic systems and measuring their performance. We then discuss and devise methods for improving these solvers. All our conclusions are supported by a variety of evidence from numerical experiments. Finally, we assess all of our methods, providing recommendations as to their use and future development.

We do achieve several things in this thesis which have not been achieved before. Firstly, we solved a non-trivial flutter problem with a direct solver. The only direct solvers that have previously been presented are those that arise from classical flutter analysis, which applies only to very simple systems. Secondly, and as an extension of this first point, we solved a system with Theodorsen aerodynamics (approximated by a highly accurately) with a direct solver. This was achieved in an industrially competitive time (0.2s). This has never before been achieved. Thirdly, we solved an unstructured multiparameter eigenvalue problem. Unstructured problems have not been considered before, even in theoretical literature. This result is thus of significance both for multiparameter spectral theory and aeroelasticity. However, the single most important contribution of this thesis is the opening of a whole new field of study which stretches beyond aeroelasticity and into other industries: the treatment of instability problems using multiparameter methods. This field of research is wide and untrodden, and has the potential to change the way we analyse instability across many industries.