Graphic Solution of a First-Order Differential Equation
Graphic Solution of a First-Order Differential Equation
This Demonstration presents Euler's method for the approximate (or graphics) solution of a first-order differential equation with initial condition , .
y'=f(x,y)
y()=
x
1
y
1
The method consists of calculating the approximation of by
y(x)
x
i+1
x
i
y
i+1
y
i
x
i
y
i
x
i
y
i
where .
i=1,…,n-1
These coordinates determine points , , …, . These points form Euler's polygonal line that is an approximate solution of the problem. The Demonstration compares it with a better solution provided by Mathematica's built-in NDSolve function (brown line).
P
1
P
2
P
n