About the book
Nonlinear differential equations are ubiquitous in computational science and engineering modelling, e.g. in fluid dynamics, finance, quantum mechanics, material science, medical applications and biology, to name only a few areas. Nowadays, the solution of challenging problems in an industrial setting requires a continuous interplay between the theoretical analysis of such systems (the investigation of the existence and stability of analytical solutions, study of bifurcation and of chaotic dynamics, etc.) and the development and use of sophisticate computational methods that can guide and support the theoretical findings by practical computer simulations. Nonlinear control theory is a prominent example, as it needs advanced mathematical techniques to interact with objects and influence their behaviour. In the past decades, owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, a rigorous solution of many applications has become possible. However, many problems still remain unsolved, and new ones continuously emerge requiring innovative solution approaches.
This book collects research papers from world leading experts in the field, highlighting ongoing trends, progress and open problems in this critically important area of mathematics and modern science.