Foundations and Computations in Dynamical Systems

Book Abstract

This Book ?Foundations and Computations in Dynamical Systems?, It is well known that the theory of dynamical systems is an essential mathematical tool in the analysis of various real-world processes and phenomena that evolve over time. Different aspects of this rich field of research are evolving all the time,including new theoretical results for qualitative investigation as well as fast numerical techniques for approximate solution. The book provides an overview of the current state of the art in this fascinating and critically important field of pure and applied mathematics, presenting recent developments in theory,modeling, algorithms, and applications. It has many applications in engineering and science. The Laplace transform techniques can be used to solve various partial differential equations and ordinary differential equations that cannot be resolved using conventional techniques. The Laplace transform approach is practically the essential functional method for engineers. The Laplace transform and variations like the fuzzy Laplace transform are advantageous because they directly solve issues such as initial value problems, fuzzy initial value problems, and non-homogeneous differential equations without first resolving the corresponding homogeneous equation. This chapter uses the Laplace transform and its variations to dynamical systems.