# Function Rrk - HP 50g User Manual

Graphing calculator.

The value of the solution, y
is appropriate for programming since it leaves the differential equation
specifications and the tolerance in the stack ready for a new solution. Notice
that the solution uses the initial conditions x = 0 at y = 0. If, your actual initial
solutions are x = x
solution provided by RKF, keeping in mind the following relationship:
The following screens show the RPN stack before and after applying function
RKF for the differential equation dy/dx = x+y, = 0.001, x = 0.1.
After applying function RKF, variable @@@y@@@ contains the value 4.3880...

## Function RRK

This function is similar to the RKF function, except that RRK (Rosenbrock and
Runge-Kutta methods) requires as the list in stack level 3 for input not only the
names of the independent and dependent variables and the function defining
the differential equation, but also the expressions for the first and second
derivatives of the expression. Thus, the input stack for this function will look as
follows:
The value in the first stack level is the value of the independent variable where
you want to find your solution, i.e., you want to find, y
represents the solution to the differential equation. The second stack level may
, will be available in variable @@@y@@@. This function
final
at y = y
, you can always add these values to the
init
init
RKF solution
x
y
0
0
x
y
final
final
{'x', 'y', 'f(x,y)' ' f/ x' ' f/ y' }
2:
1:
Actual solution
x
x
y
init
x
+ x
y
init
final
init
{
x }
x
final
final
y
init
+ y
final
= f
(x
), where f
s
final
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(x)
s