Applied Mathematical Methods

37

ODE Systems

In Chaps. 29 and 30, we conducted numerical analysis on ordinary differential equations, in singles and in systems. Further, in several intervening chapters, we went through a thorough analytical treatment of a single ODE. In this chapter and the next, we complete this study with an analytical consideration of systems of ODE’s.

Fundamental Ideas

As we have seen, a higher order ordinary differential equation (ODE) can always be converted to an appropriate number of ODE’s of the first order. As such, while studying ODE systems, without loss of generality, we can always consider the system to comprise first order ODE’s only, in the form

 

y′ = f (t,y),                     (37.1)

for which we seek a solution in the form of a vector ...