A lot of problems in science and engineering involve solving differential equations pendulums, RLC circuits, diffusion and so on. An ordinary differential equation can be expressed as:

Generally solution of this equation is of the form:

Here ‘*phi*‘ is the increment function or slope and *h* is the step size. Thus, an estimate of slope is used to extrapolate the new value *y(i+1)* when the previous value *y(i) *is known, over a distance *h*. The methods which are based on above equation are called **one step methods**. They all only differ by the definition of increment function.

**Solved Example:**

Calculate y(2) for in the interval t=[0,2]. Given y(0)=1, for

**Solution:**

Consider h=1, here

Using Euler Method: