Di erentialEquations:Theoretical and NumericalStudy

Abstract

This memory, entitled "Differential Equations : Theoretical and Numerical Study", provides a general overview of the fundamental concepts related to both ordinary and partial differential equations. It begins with the study of ordinary differential equations and progresses to linear first-order partial differential equations, emphasizing theoretical foundations and basic solution methods. The work also includes a classification of second-order PDEs, distinguishing between elliptic, parabolic, and hyperbolic types, which is essential for understanding their behavior. Finally, the thesis highlights key applications of partial differential equations in various physical contexts and touches on the importance of numerical methods in cases where analytical solutions are difficult or impossible to obtain.