Eulers Method for Single ODE

2 EULER-TYPE METHODS 5.2.1 Euler s Method for Single ODE 

The simplest numerical method for solving one ODE is called the Euler method and is based on approximating the derivative with a forward difference approximation to the derivative as follows  

The Euler approximation can be written in terms of a recurrence relation as follows  

Starting with the initial condition, this recurrence formula can be used to step forward in time as follows  

This kind of sequential calculation is called an explicit method. 

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