|
|
Contents | Previous | Next | Subchapters |
| Syntax |
[tout, yout, sout] = ode45rk(function f, ...t0, tf, y0, tol, level, smin, smax, sini)
|
| Optional |
, tol, level, smin, smax, sini
|
| See Also | ode23 , ode45 , ode4rk , odepade , odestiff |
dy
-- = f(t, y(t)) and y(t0) = y0
dt
(t, y)
This function call returns the value of f(t, y(t)) where
t is an integer, real or double-precision scalar,
and y is an integer, real or double-precision column vector
with the same length as y0.
The return value is an integer, real, double-precision or complex
vector with the same dimension as y0.
t.
t.
y(t0).
tol(j) specifies the accuracy for the elements in
the j-th column of yout.
All the elements of tol must be greater than zero.
If tol is a scalar,
it is equivalent to the case where it is a column vector with the same
length as y0 and all the elements have the value specified
by the scalar.
If tol is not present in the syntax, the default value
tol = 1d-3
t, the current step size, and the transpose
of the current value of y(t) are printed
upon completion of each successful step.
If level is not present in the syntax, the default value
level = 0
smin = (tf - t0) / 1d4
smax = (tf - t0) / 16
smin < sini < smax
sini = smax
smin < tout - tout > smax
i+1 i
ode45rk routine will try to accomplish the
requested accuracy condition which is that
for i between one and the row dimension of tout
and j between one and the row dimension of y0,
| yout - y (tout(i)) | <= tol
j j j
ode45rk.
(A continuation is where the new value of t0
is equal to the old value of tf and the new value of y0
is approximately equal to y(tf).)
y'(t) = y (t) y (0) = 0
1 2 1
y'(t) = -y (t) y (0) = 1
2 1 2
y (t) = sin(t)
1
y (t) = cos(t)
2
clear
#
function f(t, y) begin
return {y(2), -y(1)}
end
t0 = 0.
tf = 2. * pi
y0 = {0., 1.}
[tout, yout] = ode45rk(function f, t0, tf, y0)
gplot(tout, yout)
Mlmode
[, yout] = ode(yp, t0, tf, y0, tol, level)
where ode is ode23 or ode45
and the arguments tol, level are optional.
In addition, each call of the form
(t, y)
in ode45rk is translated to a call of the form
feval(yp, t, y).
yp.m in the current directory
contains the text
function dy = yp(t, y)
dy = [y(2); -y(1)];
If in Mlmode you execute the program below,
the same plot will be generated as for the ode45rk
example above.
clear
t0 = 0.;
tf = 2. * pi;
y0 = [0.; 1.];
[tout, yout] = ode45('yp', t0, tf, y0)
plot(tout, yout)