Thus, in almost all cases, it will suffice to develop and analyze numerical methods for IVPs that are written as first order vector systems in the explicit form
where
![](Images/image023.png)
The initial combination would be specified as
![](Images/image025.png)
Before proceeding with the numerical solution of the differential equation, we must ask ourselves about the existence and uniqueness of the solution of the given problem. This is stated by the following theorem: |