08.04.1
Chapter 08.04
Runge-Kutta 4th Order Method for
Ordinary Differential Equations
After reading this chapter, you should be able to
1.
develop Runge-Kutta 4
th
order method for solving ordinary differential equations,
2.
find the effect size of step size has on the solution,
3.
know the formulas for other versions of the Runge-Kutta 4
th
order method
What is the Runge-Kutta 4th order method?
Runge-Kutta 4
th
order method is a numerical technique used to solve ordinary differential
equation of the form
(
)
( )
0
0
,
,
y
y
y
x
f
dx
dy
=
=
So only first order ordinary differential equations can be solved by using the Runge-Kutta 4
th
order method.
In other sections, we have discussed how Euler and Runge-Kutta methods are
used to solve higher order ordinary differential equations or coupled (simultaneous)
differential equations.
How does one write a first order differential equation in the above form?
Example 1
Rewrite
( )
5
0
,
3
.
1
2
=
=
+
−
y
e
y
dx
dy
x
in
0
)
0
(
),
,
(
y
y
y
x
f
dx
dy
=
=
form.

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