Euler's Method

Euler's Method is a method for finding an approximation to a differential equation graphically or numerically. The solution is approximated by the tangent lines at consecutive values of x.

Example:

dy/dx = x + y
The initial condition is y(0) = 1
Let dx = .1

Using Euler's Method:

The approximation at each x value is made with the previous (x,y) values.

y_n = m_n-1( x_n - x_n-1) + y_n-1

x	m	*tan line equation*	y
0	.	.	1
.1	1	*y = 1(.1) + 1*	*1.1*
.2	*1.2*	*y = 1.2(.1) + 1.1*	*1.22*
.3	*1.52*	*y = 1.42(.1) + 1.22*	*1.362*
.4	*1.662*	*y = 1.662(.1) + 1.362*	*1.5282*

Now, a graph of the solution can be drawn, using the x and y values produced in the table.

Problems