Tip 94.
Program debugging and animation
Fig. 94. Program debugging and
animation
The
program RK4 of the
solution an ordinary differential equation (Cauchy problem) by Runge-Kutta method
of 4-th level is showed in the fig. 94. Some
operators (four operators in loop body for) are united for more compactness in
the program: (see tip 33). The program is tested on
such problem: õ′(t) = x+x2/t3
on the segment õ(0) = 1 and õ(7) = ?.
To
look at the variation the values of all local variables of the program RK4 we can as have been recommended in tip 93 – to write the variable values in arrays
and to look through them after execution of the program. But it is possible to
do it another way: to look through the values of the local variables during
execution of the program but not after! For this it will be useful resources
of animation of Mathcad.
Fig. 94a. On-line-program of
Runge-Kutta method
The
program RK4 modified in
such directions is showed in the fig. 94à:
- when we create the program we
do not use the command Add Line (technology of on-line-program – see tip 91);
- in the cycle for as the last
value of the parameter is written the system variable FRAME, that equals zero by default.
But user can change its value from 0 to 100 and look through the values of
the local variables of the program;
- the operators of the loop body
for are written in the second column of the matrix. But in the first one
there are commentaries.
The
streamlined program RK4 returns the
values of all local variables given value the variable FRAME by user.
Fig. 94b. Forming of animation
filmloop
It
is known that the variable FRAME serves for creation animation filmloops and is the counter of
frames. The process of forming the animation with help of dialogue window
Animate that is called by the same name command from the menu View is showed in
the fig. 94b. At that user points out:
·
initial
and last value of the variable FRAME (in our case they equal 0 and 100);
·
speed with
that the animation will be showed (in our case it equals three shots per
second);
·
the
area of Mathcad-document by which the animation is created (in our case it is
showed by dotted rectangle: user has enveloped in changing part of the matrix
with commentaries by broach).
After
the keystroke Animate of the same name the dialogue window in the fig. 94b
101 frame of the animation will be written: the values of the local variables n, t, k1, k2, k3, k4 and õ at different values of the variable FRAME.
Fig. 94c. The animation
filmloop during the program debugging
This
animation filmloop is showed in the fig. 94ñ. It can
be saved on the disk as avi-file. We can call it by press down Videofilmloop
(see fig. 94à). Moving the slider of the player of
the video-filmloop we can make the program RK4 to work “to all directions” – to increase and
decrease the value of the variable n. It allows to lock in some mistake easily it was done during creation
of the program.