Thesis

The theme of this thesis can be divided into two major aspects. The first is define, classify integral equations and give some methods that solve them numerically and approximately. Some examples are given, and solved numerically to illustrate the given methods. The second aspect of this thesis is to define singular integral equations and to present some methods that solve them. We solved some examples by the presented methods, also we design a flowchart and a computer program in Pascal language for each method .

The main objective of this work, is to present some aspects for construction Liapunov functions, for testing stability of linear and non-linear system with constant coefficients. New approaches and modifications of finding Liapunov functions based on new theories with illustrative problems are presented. original theory development of stability is made on the case of non-linear systems with the prove theorem used and assessed practically.